(x-3)(x-3)=2x^2-8x-15

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Solution for (x-3)(x-3)=2x^2-8x-15 equation: 


Simplifying
(x + -3)(x + -3) = 2x2 + -8x + -15

Reorder the terms:
(-3 + x)(x + -3) = 2x2 + -8x + -15

Reorder the terms:
(-3 + x)(-3 + x) = 2x2 + -8x + -15

Multiply (-3 + x) * (-3 + x)
(-3(-3 + x) + x(-3 + x)) = 2x2 + -8x + -15
((-3 * -3 + x * -3) + x(-3 + x)) = 2x2 + -8x + -15
((9 + -3x) + x(-3 + x)) = 2x2 + -8x + -15
(9 + -3x + (-3 * x + x * x)) = 2x2 + -8x + -15
(9 + -3x + (-3x + x2)) = 2x2 + -8x + -15

Combine like terms: -3x + -3x = -6x
(9 + -6x + x2) = 2x2 + -8x + -15

Reorder the terms:
9 + -6x + x2 = -15 + -8x + 2x2

Solving
9 + -6x + x2 = -15 + -8x + 2x2

Solving for variable 'x'.

Reorder the terms:
9 + 15 + -6x + 8x + x2 + -2x2 = -15 + -8x + 2x2 + 15 + 8x + -2x2

Combine like terms: 9 + 15 = 24
24 + -6x + 8x + x2 + -2x2 = -15 + -8x + 2x2 + 15 + 8x + -2x2

Combine like terms: -6x + 8x = 2x
24 + 2x + x2 + -2x2 = -15 + -8x + 2x2 + 15 + 8x + -2x2

Combine like terms: x2 + -2x2 = -1x2
24 + 2x + -1x2 = -15 + -8x + 2x2 + 15 + 8x + -2x2

Reorder the terms:
24 + 2x + -1x2 = -15 + 15 + -8x + 8x + 2x2 + -2x2

Combine like terms: -15 + 15 = 0
24 + 2x + -1x2 = 0 + -8x + 8x + 2x2 + -2x2
24 + 2x + -1x2 = -8x + 8x + 2x2 + -2x2

Combine like terms: -8x + 8x = 0
24 + 2x + -1x2 = 0 + 2x2 + -2x2
24 + 2x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
24 + 2x + -1x2 = 0

Factor a trinomial.
(6 + -1x)(4 + x) = 0


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

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {6, -4}

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