(2x-4)(2x-11)=120

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Solution for (2x-4)(2x-11)=120 equation: 


Simplifying
(2x + -4)(2x + -11) = 120

Reorder the terms:
(-4 + 2x)(2x + -11) = 120

Reorder the terms:
(-4 + 2x)(-11 + 2x) = 120

Multiply (-4 + 2x) * (-11 + 2x)
(-4(-11 + 2x) + 2x * (-11 + 2x)) = 120
((-11 * -4 + 2x * -4) + 2x * (-11 + 2x)) = 120
((44 + -8x) + 2x * (-11 + 2x)) = 120
(44 + -8x + (-11 * 2x + 2x * 2x)) = 120
(44 + -8x + (-22x + 4x2)) = 120

Combine like terms: -8x + -22x = -30x
(44 + -30x + 4x2) = 120

Solving
44 + -30x + 4x2 = 120

Solving for variable 'x'.

Reorder the terms:
44 + -120 + -30x + 4x2 = 120 + -120

Combine like terms: 44 + -120 = -76
-76 + -30x + 4x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-76 + -30x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-38 + -15x + 2x2) = 0

Factor a trinomial.
2((-2 + -1x)(19 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(19 + -2x)' equal to zero and attempt to solve:

Simplifying
19 + -2x = 0

Solving
19 + -2x = 0

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

Add '-19' to each side of the equation.
19 + -19 + -2x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -2x = 0 + -19
-2x = 0 + -19

Combine like terms: 0 + -19 = -19
-2x = -19

Divide each side by '-2'.
x = 9.5

Simplifying
x = 9.5
Solution
x = {-2, 9.5}

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