x^2+11x-17=8x+1

Solution for x^2+11x-17=8x+1 equation:

Simplifying
x2 + 11x + -17 = 8x + 1

Reorder the terms:
-17 + 11x + x2 = 8x + 1

Reorder the terms:
-17 + 11x + x2 = 1 + 8x

Solving
-17 + 11x + x2 = 1 + 8x

Solving for variable 'x'.

Reorder the terms:
-17 + -1 + 11x + -8x + x2 = 1 + 8x + -1 + -8x

Combine like terms: -17 + -1 = -18
-18 + 11x + -8x + x2 = 1 + 8x + -1 + -8x

Combine like terms: 11x + -8x = 3x
-18 + 3x + x2 = 1 + 8x + -1 + -8x

Reorder the terms:
-18 + 3x + x2 = 1 + -1 + 8x + -8x

Combine like terms: 1 + -1 = 0
-18 + 3x + x2 = 0 + 8x + -8x
-18 + 3x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-18 + 3x + x2 = 0

Factor a trinomial.
(-6 + -1x)(3 + -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 '(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
Solution
x = {-6, 3}