x^2-3x-11=8x+1

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Solution for x^2-3x-11=8x+1 equation: 


Simplifying
x2 + -3x + -11 = 8x + 1

Reorder the terms:
-11 + -3x + x2 = 8x + 1

Reorder the terms:
-11 + -3x + x2 = 1 + 8x

Solving
-11 + -3x + x2 = 1 + 8x

Solving for variable 'x'.

Reorder the terms:
-11 + -1 + -3x + -8x + x2 = 1 + 8x + -1 + -8x

Combine like terms: -11 + -1 = -12
-12 + -3x + -8x + x2 = 1 + 8x + -1 + -8x

Combine like terms: -3x + -8x = -11x
-12 + -11x + x2 = 1 + 8x + -1 + -8x

Reorder the terms:
-12 + -11x + x2 = 1 + -1 + 8x + -8x

Combine like terms: 1 + -1 = 0
-12 + -11x + x2 = 0 + 8x + -8x
-12 + -11x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-12 + -11x + x2 = 0

Factor a trinomial.
(-1 + -1x)(12 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

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

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

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-1, 12}

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