(2y-7)(4y+4)=8y-28

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Solution for (2y-7)(4y+4)=8y-28 equation: 


Simplifying
(2y + -7)(4y + 4) = 8y + -28

Reorder the terms:
(-7 + 2y)(4y + 4) = 8y + -28

Reorder the terms:
(-7 + 2y)(4 + 4y) = 8y + -28

Multiply (-7 + 2y) * (4 + 4y)
(-7(4 + 4y) + 2y * (4 + 4y)) = 8y + -28
((4 * -7 + 4y * -7) + 2y * (4 + 4y)) = 8y + -28
((-28 + -28y) + 2y * (4 + 4y)) = 8y + -28
(-28 + -28y + (4 * 2y + 4y * 2y)) = 8y + -28
(-28 + -28y + (8y + 8y2)) = 8y + -28

Combine like terms: -28y + 8y = -20y
(-28 + -20y + 8y2) = 8y + -28

Reorder the terms:
-28 + -20y + 8y2 = -28 + 8y

Add '28' to each side of the equation.
-28 + -20y + 28 + 8y2 = -28 + 28 + 8y

Reorder the terms:
-28 + 28 + -20y + 8y2 = -28 + 28 + 8y

Combine like terms: -28 + 28 = 0
0 + -20y + 8y2 = -28 + 28 + 8y
-20y + 8y2 = -28 + 28 + 8y

Combine like terms: -28 + 28 = 0
-20y + 8y2 = 0 + 8y
-20y + 8y2 = 8y

Solving
-20y + 8y2 = 8y

Solving for variable 'y'.

Reorder the terms:
-20y + -8y + 8y2 = 8y + -8y

Combine like terms: -20y + -8y = -28y
-28y + 8y2 = 8y + -8y

Combine like terms: 8y + -8y = 0
-28y + 8y2 = 0

Factor out the Greatest Common Factor (GCF), '4y'.
4y(-7 + 2y) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

Move all terms containing y to the left, all other terms to the right.

Simplifying
y = 0

Subproblem 2
Set the factor '(-7 + 2y)' equal to zero and attempt to solve:

Simplifying
-7 + 2y = 0

Solving
-7 + 2y = 0

Move all terms containing y to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + 2y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2y = 0 + 7
2y = 0 + 7

Combine like terms: 0 + 7 = 7
2y = 7

Divide each side by '2'.
y = 3.5

Simplifying
y = 3.5
Solution
y = {0, 3.5}

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