5(2x+6)(2x+6)=80

Solution for 5(2x+6)(2x+6)=80 equation:

Simplifying
5(2x + 6)(2x + 6) = 80

Reorder the terms:
5(6 + 2x)(2x + 6) = 80

Reorder the terms:
5(6 + 2x)(6 + 2x) = 80

Multiply (6 + 2x) * (6 + 2x)
5(6(6 + 2x) + 2x * (6 + 2x)) = 80
5((6 * 6 + 2x * 6) + 2x * (6 + 2x)) = 80
5((36 + 12x) + 2x * (6 + 2x)) = 80
5(36 + 12x + (6 * 2x + 2x * 2x)) = 80
5(36 + 12x + (12x + 4x2)) = 80

Combine like terms: 12x + 12x = 24x
5(36 + 24x + 4x2) = 80
(36 * 5 + 24x * 5 + 4x2 * 5) = 80
(180 + 120x + 20x2) = 80

Solving
180 + 120x + 20x2 = 80

Solving for variable 'x'.

Reorder the terms:
180 + -80 + 120x + 20x2 = 80 + -80

Combine like terms: 180 + -80 = 100
100 + 120x + 20x2 = 80 + -80

Combine like terms: 80 + -80 = 0
100 + 120x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '20'.
20(5 + 6x + x2) = 0

Factor a trinomial.
20((5 + x)(1 + x)) = 0

Ignore the factor 20.
Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

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

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

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

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {-5, -1}