x^2+3x-11=7x+1

Solution for x^2+3x-11=7x+1 equation:

Simplifying
x2 + 3x + -11 = 7x + 1

Reorder the terms:
-11 + 3x + x2 = 7x + 1

Reorder the terms:
-11 + 3x + x2 = 1 + 7x

Solving
-11 + 3x + x2 = 1 + 7x

Solving for variable 'x'.

Reorder the terms:
-11 + -1 + 3x + -7x + x2 = 1 + 7x + -1 + -7x

Combine like terms: -11 + -1 = -12
-12 + 3x + -7x + x2 = 1 + 7x + -1 + -7x

Combine like terms: 3x + -7x = -4x
-12 + -4x + x2 = 1 + 7x + -1 + -7x

Reorder the terms:
-12 + -4x + x2 = 1 + -1 + 7x + -7x

Combine like terms: 1 + -1 = 0
-12 + -4x + x2 = 0 + 7x + -7x
-12 + -4x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-12 + -4x + x2 = 0

Factor a trinomial.
(-2 + -1x)(6 + -1x) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
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
Solution
x = {-2, 6}