x^2+2x-8=3x+34

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


Simplifying
x2 + 2x + -8 = 3x + 34

Reorder the terms:
-8 + 2x + x2 = 3x + 34

Reorder the terms:
-8 + 2x + x2 = 34 + 3x

Solving
-8 + 2x + x2 = 34 + 3x

Solving for variable 'x'.

Reorder the terms:
-8 + -34 + 2x + -3x + x2 = 34 + 3x + -34 + -3x

Combine like terms: -8 + -34 = -42
-42 + 2x + -3x + x2 = 34 + 3x + -34 + -3x

Combine like terms: 2x + -3x = -1x
-42 + -1x + x2 = 34 + 3x + -34 + -3x

Reorder the terms:
-42 + -1x + x2 = 34 + -34 + 3x + -3x

Combine like terms: 34 + -34 = 0
-42 + -1x + x2 = 0 + 3x + -3x
-42 + -1x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-42 + -1x + x2 = 0

Factor a trinomial.
(-6 + -1x)(7 + -1x) = 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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-6, 7}

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