(2x+6)=(x^2-3x-18)

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


Simplifying
(2x + 6) = (x2 + -3x + -18)

Reorder the terms:
(6 + 2x) = (x2 + -3x + -18)

Remove parenthesis around (6 + 2x)
6 + 2x = (x2 + -3x + -18)

Reorder the terms:
6 + 2x = (-18 + -3x + x2)

Remove parenthesis around (-18 + -3x + x2)
6 + 2x = -18 + -3x + x2

Solving
6 + 2x = -18 + -3x + x2

Solving for variable 'x'.

Reorder the terms:
6 + 18 + 2x + 3x + -1x2 = -18 + -3x + x2 + 18 + 3x + -1x2

Combine like terms: 6 + 18 = 24
24 + 2x + 3x + -1x2 = -18 + -3x + x2 + 18 + 3x + -1x2

Combine like terms: 2x + 3x = 5x
24 + 5x + -1x2 = -18 + -3x + x2 + 18 + 3x + -1x2

Reorder the terms:
24 + 5x + -1x2 = -18 + 18 + -3x + 3x + x2 + -1x2

Combine like terms: -18 + 18 = 0
24 + 5x + -1x2 = 0 + -3x + 3x + x2 + -1x2
24 + 5x + -1x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
24 + 5x + -1x2 = 0 + x2 + -1x2
24 + 5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
24 + 5x + -1x2 = 0

Factor a trinomial.
(8 + -1x)(3 + x) = 0


Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

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

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

Divide each side by '-1'.
x = 8

Simplifying
x = 8

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {8, -3}

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