(2y-5)(2y-5)-y^2=32

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Solution for (2y-5)(2y-5)-y^2=32 equation: 


Simplifying
(2y + -5)(2y + -5) + -1y2 = 32

Reorder the terms:
(-5 + 2y)(2y + -5) + -1y2 = 32

Reorder the terms:
(-5 + 2y)(-5 + 2y) + -1y2 = 32

Multiply (-5 + 2y) * (-5 + 2y)
(-5(-5 + 2y) + 2y * (-5 + 2y)) + -1y2 = 32
((-5 * -5 + 2y * -5) + 2y * (-5 + 2y)) + -1y2 = 32
((25 + -10y) + 2y * (-5 + 2y)) + -1y2 = 32
(25 + -10y + (-5 * 2y + 2y * 2y)) + -1y2 = 32
(25 + -10y + (-10y + 4y2)) + -1y2 = 32

Combine like terms: -10y + -10y = -20y
(25 + -20y + 4y2) + -1y2 = 32

Combine like terms: 4y2 + -1y2 = 3y2
25 + -20y + 3y2 = 32

Solving
25 + -20y + 3y2 = 32

Solving for variable 'y'.

Reorder the terms:
25 + -32 + -20y + 3y2 = 32 + -32

Combine like terms: 25 + -32 = -7
-7 + -20y + 3y2 = 32 + -32

Combine like terms: 32 + -32 = 0
-7 + -20y + 3y2 = 0

Factor a trinomial.
(-1 + -3y)(7 + -1y) = 0


Subproblem 1
Set the factor '(-1 + -3y)' equal to zero and attempt to solve:

Simplifying
-1 + -3y = 0

Solving
-1 + -3y = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3y = 0 + 1
-3y = 0 + 1

Combine like terms: 0 + 1 = 1
-3y = 1

Divide each side by '-3'.
y = -0.3333333333

Simplifying
y = -0.3333333333

Subproblem 2
Set the factor '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 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 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

Simplifying
y = 7
Solution
y = {-0.3333333333, 7}

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