(2y-5)(2y-5)=9

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Solution for (2y-5)(2y-5)=9 equation: 


Simplifying
(2y + -5)(2y + -5) = 9

Reorder the terms:
(-5 + 2y)(2y + -5) = 9

Reorder the terms:
(-5 + 2y)(-5 + 2y) = 9

Multiply (-5 + 2y) * (-5 + 2y)
(-5(-5 + 2y) + 2y * (-5 + 2y)) = 9
((-5 * -5 + 2y * -5) + 2y * (-5 + 2y)) = 9
((25 + -10y) + 2y * (-5 + 2y)) = 9
(25 + -10y + (-5 * 2y + 2y * 2y)) = 9
(25 + -10y + (-10y + 4y2)) = 9

Combine like terms: -10y + -10y = -20y
(25 + -20y + 4y2) = 9

Solving
25 + -20y + 4y2 = 9

Solving for variable 'y'.

Reorder the terms:
25 + -9 + -20y + 4y2 = 9 + -9

Combine like terms: 25 + -9 = 16
16 + -20y + 4y2 = 9 + -9

Combine like terms: 9 + -9 = 0
16 + -20y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + -5y + y2) = 0

Factor a trinomial.
4((1 + -1y)(4 + -1y)) = 0

Ignore the factor 4.

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

Simplifying
1 + -1y = 0

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

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

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

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

Simplifying
y = 1

Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {1, 4}

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