2*(x-7)*(x-7)-2=0

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Solution for 2*(x-7)*(x-7)-2=0 equation: 


Simplifying
2(x + -7)(x + -7) + -2 = 0

Reorder the terms:
2(-7 + x)(x + -7) + -2 = 0

Reorder the terms:
2(-7 + x)(-7 + x) + -2 = 0

Multiply (-7 + x) * (-7 + x)
2(-7(-7 + x) + x(-7 + x)) + -2 = 0
2((-7 * -7 + x * -7) + x(-7 + x)) + -2 = 0
2((49 + -7x) + x(-7 + x)) + -2 = 0
2(49 + -7x + (-7 * x + x * x)) + -2 = 0
2(49 + -7x + (-7x + x2)) + -2 = 0

Combine like terms: -7x + -7x = -14x
2(49 + -14x + x2) + -2 = 0
(49 * 2 + -14x * 2 + x2 * 2) + -2 = 0
(98 + -28x + 2x2) + -2 = 0

Reorder the terms:
98 + -2 + -28x + 2x2 = 0

Combine like terms: 98 + -2 = 96
96 + -28x + 2x2 = 0

Solving
96 + -28x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(48 + -14x + x2) = 0

Factor a trinomial.
2((6 + -1x)(8 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {6, 8}

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