(x-3)(x-3)=2x^2-2x-12

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Solution for (x-3)(x-3)=2x^2-2x-12 equation: 


Simplifying
(x + -3)(x + -3) = 2x2 + -2x + -12

Reorder the terms:
(-3 + x)(x + -3) = 2x2 + -2x + -12

Reorder the terms:
(-3 + x)(-3 + x) = 2x2 + -2x + -12

Multiply (-3 + x) * (-3 + x)
(-3(-3 + x) + x(-3 + x)) = 2x2 + -2x + -12
((-3 * -3 + x * -3) + x(-3 + x)) = 2x2 + -2x + -12
((9 + -3x) + x(-3 + x)) = 2x2 + -2x + -12
(9 + -3x + (-3 * x + x * x)) = 2x2 + -2x + -12
(9 + -3x + (-3x + x2)) = 2x2 + -2x + -12

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

Reorder the terms:
9 + -6x + x2 = -12 + -2x + 2x2

Solving
9 + -6x + x2 = -12 + -2x + 2x2

Solving for variable 'x'.

Reorder the terms:
9 + 12 + -6x + 2x + x2 + -2x2 = -12 + -2x + 2x2 + 12 + 2x + -2x2

Combine like terms: 9 + 12 = 21
21 + -6x + 2x + x2 + -2x2 = -12 + -2x + 2x2 + 12 + 2x + -2x2

Combine like terms: -6x + 2x = -4x
21 + -4x + x2 + -2x2 = -12 + -2x + 2x2 + 12 + 2x + -2x2

Combine like terms: x2 + -2x2 = -1x2
21 + -4x + -1x2 = -12 + -2x + 2x2 + 12 + 2x + -2x2

Reorder the terms:
21 + -4x + -1x2 = -12 + 12 + -2x + 2x + 2x2 + -2x2

Combine like terms: -12 + 12 = 0
21 + -4x + -1x2 = 0 + -2x + 2x + 2x2 + -2x2
21 + -4x + -1x2 = -2x + 2x + 2x2 + -2x2

Combine like terms: -2x + 2x = 0
21 + -4x + -1x2 = 0 + 2x2 + -2x2
21 + -4x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
21 + -4x + -1x2 = 0

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


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 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 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 + x = 0 + -7

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

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

Simplifying
x = -7
Solution
x = {3, -7}

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