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

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


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

Reorder the terms for easier multiplication:
x2 = (2x + -8)(x + -3)

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

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

Multiply (-8 + 2x) * (-3 + x)
x2 = (-8(-3 + x) + 2x * (-3 + x))
x2 = ((-3 * -8 + x * -8) + 2x * (-3 + x))
x2 = ((24 + -8x) + 2x * (-3 + x))
x2 = (24 + -8x + (-3 * 2x + x * 2x))
x2 = (24 + -8x + (-6x + 2x2))

Combine like terms: -8x + -6x = -14x
x2 = (24 + -14x + 2x2)

Solving
x2 = 24 + -14x + 2x2

Solving for variable 'x'.

Reorder the terms:
-24 + 14x + x2 + -2x2 = 24 + -14x + 2x2 + -24 + 14x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-24 + 14x + -1x2 = 24 + -14x + 2x2 + -24 + 14x + -2x2

Reorder the terms:
-24 + 14x + -1x2 = 24 + -24 + -14x + 14x + 2x2 + -2x2

Combine like terms: 24 + -24 = 0
-24 + 14x + -1x2 = 0 + -14x + 14x + 2x2 + -2x2
-24 + 14x + -1x2 = -14x + 14x + 2x2 + -2x2

Combine like terms: -14x + 14x = 0
-24 + 14x + -1x2 = 0 + 2x2 + -2x2
-24 + 14x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-24 + 14x + -1x2 = 0

Factor a trinomial.
(-12 + x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-12 + x)' equal to zero and attempt to solve:

Simplifying
-12 + x = 0

Solving
-12 + x = 0

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

Add '12' to each side of the equation.
-12 + 12 + x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + x = 0 + 12
x = 0 + 12

Combine like terms: 0 + 12 = 12
x = 12

Simplifying
x = 12

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {12, 2}

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