(2y+5)(2y+5)=25

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Solution for (2y+5)(2y+5)=25 equation: 


Simplifying
(2y + 5)(2y + 5) = 25

Reorder the terms:
(5 + 2y)(2y + 5) = 25

Reorder the terms:
(5 + 2y)(5 + 2y) = 25

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

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

Add '-25' to each side of the equation.
25 + 20y + -25 + 4y2 = 25 + -25

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

Combine like terms: 25 + -25 = 0
0 + 20y + 4y2 = 25 + -25
20y + 4y2 = 25 + -25

Combine like terms: 25 + -25 = 0
20y + 4y2 = 0

Solving
20y + 4y2 = 0

Solving for variable 'y'.

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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