(2x-4)(x-4)2=1440

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Solution for (2x-4)(x-4)2=1440 equation: 


Simplifying
(2x + -4)(x + -4) * 2 = 1440

Reorder the terms:
(-4 + 2x)(x + -4) * 2 = 1440

Reorder the terms:
(-4 + 2x)(-4 + x) * 2 = 1440

Reorder the terms for easier multiplication:
2(-4 + 2x)(-4 + x) = 1440

Multiply (-4 + 2x) * (-4 + x)
2(-4(-4 + x) + 2x * (-4 + x)) = 1440
2((-4 * -4 + x * -4) + 2x * (-4 + x)) = 1440
2((16 + -4x) + 2x * (-4 + x)) = 1440
2(16 + -4x + (-4 * 2x + x * 2x)) = 1440
2(16 + -4x + (-8x + 2x2)) = 1440

Combine like terms: -4x + -8x = -12x
2(16 + -12x + 2x2) = 1440
(16 * 2 + -12x * 2 + 2x2 * 2) = 1440
(32 + -24x + 4x2) = 1440

Solving
32 + -24x + 4x2 = 1440

Solving for variable 'x'.

Reorder the terms:
32 + -1440 + -24x + 4x2 = 1440 + -1440

Combine like terms: 32 + -1440 = -1408
-1408 + -24x + 4x2 = 1440 + -1440

Combine like terms: 1440 + -1440 = 0
-1408 + -24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-352 + -6x + x2) = 0

Factor a trinomial.
4((-16 + -1x)(22 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-16 + -1x)' equal to zero and attempt to solve:

Simplifying
-16 + -1x = 0

Solving
-16 + -1x = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1x = 0 + 16
-1x = 0 + 16

Combine like terms: 0 + 16 = 16
-1x = 16

Divide each side by '-1'.
x = -16

Simplifying
x = -16

Subproblem 2
Set the factor '(22 + -1x)' equal to zero and attempt to solve:

Simplifying
22 + -1x = 0

Solving
22 + -1x = 0

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

Add '-22' to each side of the equation.
22 + -22 + -1x = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -1x = 0 + -22
-1x = 0 + -22

Combine like terms: 0 + -22 = -22
-1x = -22

Divide each side by '-1'.
x = 22

Simplifying
x = 22
Solution
x = {-16, 22}

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