(y+5)(y+5)=100

Solution for (y+5)(y+5)=100 equation:

Simplifying
(y + 5)(y + 5) = 100

Reorder the terms:
(5 + y)(y + 5) = 100

Reorder the terms:
(5 + y)(5 + y) = 100

Multiply (5 + y) * (5 + y)
(5(5 + y) + y(5 + y)) = 100
((5 * 5 + y * 5) + y(5 + y)) = 100
((25 + 5y) + y(5 + y)) = 100
(25 + 5y + (5 * y + y * y)) = 100
(25 + 5y + (5y + y2)) = 100

Combine like terms: 5y + 5y = 10y
(25 + 10y + y2) = 100

Solving
25 + 10y + y2 = 100

Solving for variable 'y'.

Reorder the terms:
25 + -100 + 10y + y2 = 100 + -100

Combine like terms: 25 + -100 = -75
-75 + 10y + y2 = 100 + -100

Combine like terms: 100 + -100 = 0
-75 + 10y + y2 = 0

Factor a trinomial.
(-15 + -1y)(5 + -1y) = 0

Subproblem 1
Set the factor '(-15 + -1y)' equal to zero and attempt to solve:

Simplifying
-15 + -1y = 0

Solving
-15 + -1y = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1y = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1y = 0 + 15
-1y = 0 + 15

Combine like terms: 0 + 15 = 15
-1y = 15

Divide each side by '-1'.
y = -15

Simplifying
y = -15
Subproblem 2
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 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 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Solution
y = {-15, 5}