(2y-3)(2y+3)=20y-9

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Solution for (2y-3)(2y+3)=20y-9 equation: 


Simplifying
(2y + -3)(2y + 3) = 20y + -9

Reorder the terms:
(-3 + 2y)(2y + 3) = 20y + -9

Reorder the terms:
(-3 + 2y)(3 + 2y) = 20y + -9

Multiply (-3 + 2y) * (3 + 2y)
(-3(3 + 2y) + 2y * (3 + 2y)) = 20y + -9
((3 * -3 + 2y * -3) + 2y * (3 + 2y)) = 20y + -9
((-9 + -6y) + 2y * (3 + 2y)) = 20y + -9
(-9 + -6y + (3 * 2y + 2y * 2y)) = 20y + -9
(-9 + -6y + (6y + 4y2)) = 20y + -9

Combine like terms: -6y + 6y = 0
(-9 + 0 + 4y2) = 20y + -9
(-9 + 4y2) = 20y + -9

Reorder the terms:
-9 + 4y2 = -9 + 20y

Add '9' to each side of the equation.
-9 + 9 + 4y2 = -9 + 9 + 20y

Combine like terms: -9 + 9 = 0
0 + 4y2 = -9 + 9 + 20y
4y2 = -9 + 9 + 20y

Combine like terms: -9 + 9 = 0
4y2 = 0 + 20y
4y2 = 20y

Solving
4y2 = 20y

Solving for variable 'y'.

Reorder the terms:
-20y + 4y2 = 20y + -20y

Combine like terms: 20y + -20y = 0
-20y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '4y'.
4y(-5 + y) = 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 '(-5 + y)' equal to zero and attempt to solve:

Simplifying
-5 + y = 0

Solving
-5 + y = 0

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

Add '5' to each side of the equation.
-5 + 5 + y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + y = 0 + 5
y = 0 + 5

Combine like terms: 0 + 5 = 5
y = 5

Simplifying
y = 5
Solution
y = {0, 5}

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