2(x-5)(x-5)-8=0

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Solution for 2(x-5)(x-5)-8=0 equation: 


Simplifying
2(x + -5)(x + -5) + -8 = 0

Reorder the terms:
2(-5 + x)(x + -5) + -8 = 0

Reorder the terms:
2(-5 + x)(-5 + x) + -8 = 0

Multiply (-5 + x) * (-5 + x)
2(-5(-5 + x) + x(-5 + x)) + -8 = 0
2((-5 * -5 + x * -5) + x(-5 + x)) + -8 = 0
2((25 + -5x) + x(-5 + x)) + -8 = 0
2(25 + -5x + (-5 * x + x * x)) + -8 = 0
2(25 + -5x + (-5x + x2)) + -8 = 0

Combine like terms: -5x + -5x = -10x
2(25 + -10x + x2) + -8 = 0
(25 * 2 + -10x * 2 + x2 * 2) + -8 = 0
(50 + -20x + 2x2) + -8 = 0

Reorder the terms:
50 + -8 + -20x + 2x2 = 0

Combine like terms: 50 + -8 = 42
42 + -20x + 2x2 = 0

Solving
42 + -20x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + -10x + x2) = 0

Factor a trinomial.
2((3 + -1x)(7 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

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 = {3, 7}

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