12x-24+8x+16=x^2+18x-16

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Solution for 12x-24+8x+16=x^2+18x-16 equation: 


Simplifying
12x + -24 + 8x + 16 = x2 + 18x + -16

Reorder the terms:
-24 + 16 + 12x + 8x = x2 + 18x + -16

Combine like terms: -24 + 16 = -8
-8 + 12x + 8x = x2 + 18x + -16

Combine like terms: 12x + 8x = 20x
-8 + 20x = x2 + 18x + -16

Reorder the terms:
-8 + 20x = -16 + 18x + x2

Solving
-8 + 20x = -16 + 18x + x2

Solving for variable 'x'.

Reorder the terms:
-8 + 16 + 20x + -18x + -1x2 = -16 + 18x + x2 + 16 + -18x + -1x2

Combine like terms: -8 + 16 = 8
8 + 20x + -18x + -1x2 = -16 + 18x + x2 + 16 + -18x + -1x2

Combine like terms: 20x + -18x = 2x
8 + 2x + -1x2 = -16 + 18x + x2 + 16 + -18x + -1x2

Reorder the terms:
8 + 2x + -1x2 = -16 + 16 + 18x + -18x + x2 + -1x2

Combine like terms: -16 + 16 = 0
8 + 2x + -1x2 = 0 + 18x + -18x + x2 + -1x2
8 + 2x + -1x2 = 18x + -18x + x2 + -1x2

Combine like terms: 18x + -18x = 0
8 + 2x + -1x2 = 0 + x2 + -1x2
8 + 2x + -1x2 = x2 + -1x2

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

Factor a trinomial.
(4 + -1x)(2 + x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {4, -2}

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