2(x-4)(x-4)=18

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Solution for 2(x-4)(x-4)=18 equation: 


Simplifying
2(x + -4)(x + -4) = 18

Reorder the terms:
2(-4 + x)(x + -4) = 18

Reorder the terms:
2(-4 + x)(-4 + x) = 18

Multiply (-4 + x) * (-4 + x)
2(-4(-4 + x) + x(-4 + x)) = 18
2((-4 * -4 + x * -4) + x(-4 + x)) = 18
2((16 + -4x) + x(-4 + x)) = 18
2(16 + -4x + (-4 * x + x * x)) = 18
2(16 + -4x + (-4x + x2)) = 18

Combine like terms: -4x + -4x = -8x
2(16 + -8x + x2) = 18
(16 * 2 + -8x * 2 + x2 * 2) = 18
(32 + -16x + 2x2) = 18

Solving
32 + -16x + 2x2 = 18

Solving for variable 'x'.

Reorder the terms:
32 + -18 + -16x + 2x2 = 18 + -18

Combine like terms: 32 + -18 = 14
14 + -16x + 2x2 = 18 + -18

Combine like terms: 18 + -18 = 0
14 + -16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -8x + x2) = 0

Factor a trinomial.
2((1 + -1x)(7 + -1x)) = 0

Ignore the factor 2.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {1, 7}

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