x-6=x^2-3x-18

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Solution for x-6=x^2-3x-18 equation: 


Simplifying
x + -6 = x2 + -3x + -18

Reorder the terms:
-6 + x = x2 + -3x + -18

Reorder the terms:
-6 + x = -18 + -3x + x2

Solving
-6 + x = -18 + -3x + x2

Solving for variable 'x'.

Reorder the terms:
-6 + 18 + x + 3x + -1x2 = -18 + -3x + x2 + 18 + 3x + -1x2

Combine like terms: -6 + 18 = 12
12 + x + 3x + -1x2 = -18 + -3x + x2 + 18 + 3x + -1x2

Combine like terms: x + 3x = 4x
12 + 4x + -1x2 = -18 + -3x + x2 + 18 + 3x + -1x2

Reorder the terms:
12 + 4x + -1x2 = -18 + 18 + -3x + 3x + x2 + -1x2

Combine like terms: -18 + 18 = 0
12 + 4x + -1x2 = 0 + -3x + 3x + x2 + -1x2
12 + 4x + -1x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
12 + 4x + -1x2 = 0 + x2 + -1x2
12 + 4x + -1x2 = x2 + -1x2

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

Factor a trinomial.
(6 + -1x)(2 + 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 '(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 = {6, -2}

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