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Simplifying
18m2 + 6m + 6 = 6m2 + 30m + -3

Reorder the terms:
6 + 6m + 18m2 = 6m2 + 30m + -3

Reorder the terms:
6 + 6m + 18m2 = -3 + 30m + 6m2

Solving
6 + 6m + 18m2 = -3 + 30m + 6m2

Solving for variable 'm'.

Reorder the terms:
6 + 3 + 6m + -30m + 18m2 + -6m2 = -3 + 30m + 6m2 + 3 + -30m + -6m2

Combine like terms: 6 + 3 = 9
9 + 6m + -30m + 18m2 + -6m2 = -3 + 30m + 6m2 + 3 + -30m + -6m2

Combine like terms: 6m + -30m = -24m
9 + -24m + 18m2 + -6m2 = -3 + 30m + 6m2 + 3 + -30m + -6m2

Combine like terms: 18m2 + -6m2 = 12m2
9 + -24m + 12m2 = -3 + 30m + 6m2 + 3 + -30m + -6m2

Reorder the terms:
9 + -24m + 12m2 = -3 + 3 + 30m + -30m + 6m2 + -6m2

Combine like terms: -3 + 3 = 0
9 + -24m + 12m2 = 0 + 30m + -30m + 6m2 + -6m2
9 + -24m + 12m2 = 30m + -30m + 6m2 + -6m2

Combine like terms: 30m + -30m = 0
9 + -24m + 12m2 = 0 + 6m2 + -6m2
9 + -24m + 12m2 = 6m2 + -6m2

Combine like terms: 6m2 + -6m2 = 0
9 + -24m + 12m2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -8m + 4m2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(3 + -8m + 4m2)' equal to zero and attempt to solve: Simplifying 3 + -8m + 4m2 = 0 Solving 3 + -8m + 4m2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + -2m + m2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -2m + -0.75 + m2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -2m + m2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -2m + m2 = 0 + -0.75 -2m + m2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -2m + m2 = -0.75 The m term is -2m. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2m + 1 + m2 = -0.75 + 1 Reorder the terms: 1 + -2m + m2 = -0.75 + 1 Combine like terms: -0.75 + 1 = 0.25 1 + -2m + m2 = 0.25 Factor a perfect square on the left side: (m + -1)(m + -1) = 0.25 Calculate the square root of the right side: 0.5 Break this problem into two subproblems by setting (m + -1) equal to 0.5 and -0.5.

Subproblem 1

m + -1 = 0.5 Simplifying m + -1 = 0.5 Reorder the terms: -1 + m = 0.5 Solving -1 + m = 0.5 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = 0.5 + 1 Combine like terms: -1 + 1 = 0 0 + m = 0.5 + 1 m = 0.5 + 1 Combine like terms: 0.5 + 1 = 1.5 m = 1.5 Simplifying m = 1.5

Subproblem 2

m + -1 = -0.5 Simplifying m + -1 = -0.5 Reorder the terms: -1 + m = -0.5 Solving -1 + m = -0.5 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = -0.5 + 1 Combine like terms: -1 + 1 = 0 0 + m = -0.5 + 1 m = -0.5 + 1 Combine like terms: -0.5 + 1 = 0.5 m = 0.5 Simplifying m = 0.5

Solution

The solution to the problem is based on the solutions from the subproblems. m = {1.5, 0.5}

Solution

m = {1.5, 0.5}
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