x^2-8x-30=12+3x

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Solution for x^2-8x-30=12+3x equation: 


Simplifying
x2 + -8x + -30 = 12 + 3x

Reorder the terms:
-30 + -8x + x2 = 12 + 3x

Solving
-30 + -8x + x2 = 12 + 3x

Solving for variable 'x'.

Reorder the terms:
-30 + -12 + -8x + -3x + x2 = 12 + 3x + -12 + -3x

Combine like terms: -30 + -12 = -42
-42 + -8x + -3x + x2 = 12 + 3x + -12 + -3x

Combine like terms: -8x + -3x = -11x
-42 + -11x + x2 = 12 + 3x + -12 + -3x

Reorder the terms:
-42 + -11x + x2 = 12 + -12 + 3x + -3x

Combine like terms: 12 + -12 = 0
-42 + -11x + x2 = 0 + 3x + -3x
-42 + -11x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-42 + -11x + x2 = 0

Factor a trinomial.
(-3 + -1x)(14 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Solution
x = {-3, 14}

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