(x-6)(3x+7)=-11x+1

Solution for (x-6)(3x+7)=-11x+1 equation:

Simplifying
(x + -6)(3x + 7) = -11x + 1

Reorder the terms:
(-6 + x)(3x + 7) = -11x + 1

Reorder the terms:
(-6 + x)(7 + 3x) = -11x + 1

Multiply (-6 + x) * (7 + 3x)
(-6(7 + 3x) + x(7 + 3x)) = -11x + 1
((7 * -6 + 3x * -6) + x(7 + 3x)) = -11x + 1
((-42 + -18x) + x(7 + 3x)) = -11x + 1
(-42 + -18x + (7 * x + 3x * x)) = -11x + 1
(-42 + -18x + (7x + 3x2)) = -11x + 1

Combine like terms: -18x + 7x = -11x
(-42 + -11x + 3x2) = -11x + 1

Reorder the terms:
-42 + -11x + 3x2 = 1 + -11x

Add '11x' to each side of the equation.
-42 + -11x + 11x + 3x2 = 1 + -11x + 11x

Combine like terms: -11x + 11x = 0
-42 + 0 + 3x2 = 1 + -11x + 11x
-42 + 3x2 = 1 + -11x + 11x

Combine like terms: -11x + 11x = 0
-42 + 3x2 = 1 + 0
-42 + 3x2 = 1

Solving
-42 + 3x2 = 1

Solving for variable 'x'.

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

Add '42' to each side of the equation.
-42 + 42 + 3x2 = 1 + 42

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

Combine like terms: 1 + 42 = 43
3x2 = 43

Divide each side by '3'.
x2 = 14.33333333

Simplifying
x2 = 14.33333333

Take the square root of each side:
x = {-3.785938897, 3.785938897}