(8y+4)(4y+8)=36

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Solution for (8y+4)(4y+8)=36 equation:


Simplifying
(8y + 4)(4y + 8) = 36

Reorder the terms:
(4 + 8y)(4y + 8) = 36

Reorder the terms:
(4 + 8y)(8 + 4y) = 36

Multiply (4 + 8y) * (8 + 4y)
(4(8 + 4y) + 8y * (8 + 4y)) = 36
((8 * 4 + 4y * 4) + 8y * (8 + 4y)) = 36
((32 + 16y) + 8y * (8 + 4y)) = 36
(32 + 16y + (8 * 8y + 4y * 8y)) = 36
(32 + 16y + (64y + 32y2)) = 36

Combine like terms: 16y + 64y = 80y
(32 + 80y + 32y2) = 36

Solving
32 + 80y + 32y2 = 36

Solving for variable 'y'.

Reorder the terms:
32 + -36 + 80y + 32y2 = 36 + -36

Combine like terms: 32 + -36 = -4
-4 + 80y + 32y2 = 36 + -36

Combine like terms: 36 + -36 = 0
-4 + 80y + 32y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 20y + 8y2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-1 + 20y + 8y2)' equal to zero and attempt to solve: Simplifying -1 + 20y + 8y2 = 0 Solving -1 + 20y + 8y2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + 2.5y + y2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + 2.5y + 0.125 + y2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + 2.5y + y2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + 2.5y + y2 = 0 + 0.125 2.5y + y2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 2.5y + y2 = 0.125 The y term is 2.5y. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5y + 1.5625 + y2 = 0.125 + 1.5625 Reorder the terms: 1.5625 + 2.5y + y2 = 0.125 + 1.5625 Combine like terms: 0.125 + 1.5625 = 1.6875 1.5625 + 2.5y + y2 = 1.6875 Factor a perfect square on the left side: (y + 1.25)(y + 1.25) = 1.6875 Calculate the square root of the right side: 1.299038106 Break this problem into two subproblems by setting (y + 1.25) equal to 1.299038106 and -1.299038106.

Subproblem 1

y + 1.25 = 1.299038106 Simplifying y + 1.25 = 1.299038106 Reorder the terms: 1.25 + y = 1.299038106 Solving 1.25 + y = 1.299038106 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + y = 1.299038106 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + y = 1.299038106 + -1.25 y = 1.299038106 + -1.25 Combine like terms: 1.299038106 + -1.25 = 0.049038106 y = 0.049038106 Simplifying y = 0.049038106

Subproblem 2

y + 1.25 = -1.299038106 Simplifying y + 1.25 = -1.299038106 Reorder the terms: 1.25 + y = -1.299038106 Solving 1.25 + y = -1.299038106 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + y = -1.299038106 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + y = -1.299038106 + -1.25 y = -1.299038106 + -1.25 Combine like terms: -1.299038106 + -1.25 = -2.549038106 y = -2.549038106 Simplifying y = -2.549038106

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.049038106, -2.549038106}

Solution

y = {0.049038106, -2.549038106}

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