2(x-3)(x-3)-8=0

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Solution for 2(x-3)(x-3)-8=0 equation: 


Simplifying
2(x + -3)(x + -3) + -8 = 0

Reorder the terms:
2(-3 + x)(x + -3) + -8 = 0

Reorder the terms:
2(-3 + x)(-3 + x) + -8 = 0

Multiply (-3 + x) * (-3 + x)
2(-3(-3 + x) + x(-3 + x)) + -8 = 0
2((-3 * -3 + x * -3) + x(-3 + x)) + -8 = 0
2((9 + -3x) + x(-3 + x)) + -8 = 0
2(9 + -3x + (-3 * x + x * x)) + -8 = 0
2(9 + -3x + (-3x + x2)) + -8 = 0

Combine like terms: -3x + -3x = -6x
2(9 + -6x + x2) + -8 = 0
(9 * 2 + -6x * 2 + x2 * 2) + -8 = 0
(18 + -12x + 2x2) + -8 = 0

Reorder the terms:
18 + -8 + -12x + 2x2 = 0

Combine like terms: 18 + -8 = 10
10 + -12x + 2x2 = 0

Solving
10 + -12x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -6x + x2) = 0

Factor a trinomial.
2((1 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {1, 5}

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