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Simplifying
8y2 + 10y + -3 = 0

Reorder the terms:
-3 + 10y + 8y2 = 0

Solving
-3 + 10y + 8y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
-0.375 + 1.25y + y2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + 1.25y + 0.375 + y2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + 1.25y + y2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + 1.25y + y2 = 0 + 0.375
1.25y + y2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
1.25y + y2 = 0.375

The y term is 1.25y.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25y + 0.390625 + y2 = 0.375 + 0.390625

Reorder the terms:
0.390625 + 1.25y + y2 = 0.375 + 0.390625

Combine like terms: 0.375 + 0.390625 = 0.765625
0.390625 + 1.25y + y2 = 0.765625

Factor a perfect square on the left side:
(y + 0.625)(y + 0.625) = 0.765625

Calculate the square root of the right side: 0.875

Break this problem into two subproblems by setting 
(y + 0.625) equal to 0.875 and -0.875.

Subproblem 1

y + 0.625 = 0.875 Simplifying y + 0.625 = 0.875 Reorder the terms: 0.625 + y = 0.875 Solving 0.625 + y = 0.875 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + y = 0.875 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + y = 0.875 + -0.625 y = 0.875 + -0.625 Combine like terms: 0.875 + -0.625 = 0.25 y = 0.25 Simplifying y = 0.25

Subproblem 2

y + 0.625 = -0.875 Simplifying y + 0.625 = -0.875 Reorder the terms: 0.625 + y = -0.875 Solving 0.625 + y = -0.875 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + y = -0.875 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + y = -0.875 + -0.625 y = -0.875 + -0.625 Combine like terms: -0.875 + -0.625 = -1.5 y = -1.5 Simplifying y = -1.5

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.25, -1.5}
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