x^2+12x-34=3(x-8)

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Solution for x^2+12x-34=3(x-8) equation: 


Simplifying
x2 + 12x + -34 = 3(x + -8)

Reorder the terms:
-34 + 12x + x2 = 3(x + -8)

Reorder the terms:
-34 + 12x + x2 = 3(-8 + x)
-34 + 12x + x2 = (-8 * 3 + x * 3)
-34 + 12x + x2 = (-24 + 3x)

Solving
-34 + 12x + x2 = -24 + 3x

Solving for variable 'x'.

Reorder the terms:
-34 + 24 + 12x + -3x + x2 = -24 + 3x + 24 + -3x

Combine like terms: -34 + 24 = -10
-10 + 12x + -3x + x2 = -24 + 3x + 24 + -3x

Combine like terms: 12x + -3x = 9x
-10 + 9x + x2 = -24 + 3x + 24 + -3x

Reorder the terms:
-10 + 9x + x2 = -24 + 24 + 3x + -3x

Combine like terms: -24 + 24 = 0
-10 + 9x + x2 = 0 + 3x + -3x
-10 + 9x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-10 + 9x + x2 = 0

Factor a trinomial.
(-10 + -1x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-10, 1}

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