(2x-4)(x-4)=448

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Solution for (2x-4)(x-4)=448 equation:


Simplifying
(2x + -4)(x + -4) = 448

Reorder the terms:
(-4 + 2x)(x + -4) = 448

Reorder the terms:
(-4 + 2x)(-4 + x) = 448

Multiply (-4 + 2x) * (-4 + x)
(-4(-4 + x) + 2x * (-4 + x)) = 448
((-4 * -4 + x * -4) + 2x * (-4 + x)) = 448
((16 + -4x) + 2x * (-4 + x)) = 448
(16 + -4x + (-4 * 2x + x * 2x)) = 448
(16 + -4x + (-8x + 2x2)) = 448

Combine like terms: -4x + -8x = -12x
(16 + -12x + 2x2) = 448

Solving
16 + -12x + 2x2 = 448

Solving for variable 'x'.

Reorder the terms:
16 + -448 + -12x + 2x2 = 448 + -448

Combine like terms: 16 + -448 = -432
-432 + -12x + 2x2 = 448 + -448

Combine like terms: 448 + -448 = 0
-432 + -12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-216 + -6x + x2) = 0

Factor a trinomial.
2((-12 + -1x)(18 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12

Subproblem 2
Set the factor '(18 + -1x)' equal to zero and attempt to solve:

Simplifying
18 + -1x = 0

Solving
18 + -1x = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1x = 0 + -18
-1x = 0 + -18

Combine like terms: 0 + -18 = -18
-1x = -18

Divide each side by '-1'.
x = 18

Simplifying
x = 18
Solution
x = {-12, 18}

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