(2x+6)(2x+8)=120

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Solution for (2x+6)(2x+8)=120 equation: 


Simplifying
(2x + 6)(2x + 8) = 120

Reorder the terms:
(6 + 2x)(2x + 8) = 120

Reorder the terms:
(6 + 2x)(8 + 2x) = 120

Multiply (6 + 2x) * (8 + 2x)
(6(8 + 2x) + 2x * (8 + 2x)) = 120
((8 * 6 + 2x * 6) + 2x * (8 + 2x)) = 120
((48 + 12x) + 2x * (8 + 2x)) = 120
(48 + 12x + (8 * 2x + 2x * 2x)) = 120
(48 + 12x + (16x + 4x2)) = 120

Combine like terms: 12x + 16x = 28x
(48 + 28x + 4x2) = 120

Solving
48 + 28x + 4x2 = 120

Solving for variable 'x'.

Reorder the terms:
48 + -120 + 28x + 4x2 = 120 + -120

Combine like terms: 48 + -120 = -72
-72 + 28x + 4x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-72 + 28x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + 7x + x2) = 0

Factor a trinomial.
4((-9 + -1x)(2 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-9, 2}

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