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

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

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

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

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

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

Combine like terms: -6x + 7x = 1x
(-42 + 1x + x2) = (x + 3)(x + -11)

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

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

Multiply (3 + x) * (-11 + x)
-42 + 1x + x2 = (3(-11 + x) + x(-11 + x))
-42 + 1x + x2 = ((-11 * 3 + x * 3) + x(-11 + x))
-42 + 1x + x2 = ((-33 + 3x) + x(-11 + x))
-42 + 1x + x2 = (-33 + 3x + (-11 * x + x * x))
-42 + 1x + x2 = (-33 + 3x + (-11x + x2))

Combine like terms: 3x + -11x = -8x
-42 + 1x + x2 = (-33 + -8x + x2)

Add '-1x2' to each side of the equation.
-42 + 1x + x2 + -1x2 = -33 + -8x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-42 + 1x + 0 = -33 + -8x + x2 + -1x2
-42 + 1x = -33 + -8x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-42 + 1x = -33 + -8x + 0
-42 + 1x = -33 + -8x

Solving
-42 + 1x = -33 + -8x

Solving for variable 'x'.

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

Add '8x' to each side of the equation.
-42 + 1x + 8x = -33 + -8x + 8x

Combine like terms: 1x + 8x = 9x
-42 + 9x = -33 + -8x + 8x

Combine like terms: -8x + 8x = 0
-42 + 9x = -33 + 0
-42 + 9x = -33

Add '42' to each side of the equation.
-42 + 42 + 9x = -33 + 42

Combine like terms: -42 + 42 = 0
0 + 9x = -33 + 42
9x = -33 + 42

Combine like terms: -33 + 42 = 9
9x = 9

Divide each side by '9'.
x = 1

Simplifying
x = 1