(x-5)(x+4)=(x+7)(x-6)

Solution for (x-5)(x+4)=(x+7)(x-6) equation:

Simplifying
(x + -5)(x + 4) = (x + 7)(x + -6)

Reorder the terms:
(-5 + x)(x + 4) = (x + 7)(x + -6)

Reorder the terms:
(-5 + x)(4 + x) = (x + 7)(x + -6)

Multiply (-5 + x) * (4 + x)
(-5(4 + x) + x(4 + x)) = (x + 7)(x + -6)
((4 * -5 + x * -5) + x(4 + x)) = (x + 7)(x + -6)
((-20 + -5x) + x(4 + x)) = (x + 7)(x + -6)
(-20 + -5x + (4 * x + x * x)) = (x + 7)(x + -6)
(-20 + -5x + (4x + x2)) = (x + 7)(x + -6)

Combine like terms: -5x + 4x = -1x
(-20 + -1x + x2) = (x + 7)(x + -6)

Reorder the terms:
-20 + -1x + x2 = (7 + x)(x + -6)

Reorder the terms:
-20 + -1x + x2 = (7 + x)(-6 + x)

Multiply (7 + x) * (-6 + x)
-20 + -1x + x2 = (7(-6 + x) + x(-6 + x))
-20 + -1x + x2 = ((-6 * 7 + x * 7) + x(-6 + x))
-20 + -1x + x2 = ((-42 + 7x) + x(-6 + x))
-20 + -1x + x2 = (-42 + 7x + (-6 * x + x * x))
-20 + -1x + x2 = (-42 + 7x + (-6x + x2))

Combine like terms: 7x + -6x = 1x
-20 + -1x + x2 = (-42 + 1x + x2)

Add '-1x2' to each side of the equation.
-20 + -1x + x2 + -1x2 = -42 + 1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-20 + -1x + 0 = -42 + 1x + x2 + -1x2
-20 + -1x = -42 + 1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-20 + -1x = -42 + 1x + 0
-20 + -1x = -42 + 1x

Solving
-20 + -1x = -42 + 1x

Solving for variable 'x'.

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

Add '-1x' to each side of the equation.
-20 + -1x + -1x = -42 + 1x + -1x

Combine like terms: -1x + -1x = -2x
-20 + -2x = -42 + 1x + -1x

Combine like terms: 1x + -1x = 0
-20 + -2x = -42 + 0
-20 + -2x = -42

Add '20' to each side of the equation.
-20 + 20 + -2x = -42 + 20

Combine like terms: -20 + 20 = 0
0 + -2x = -42 + 20
-2x = -42 + 20

Combine like terms: -42 + 20 = -22
-2x = -22

Divide each side by '-2'.
x = 11

Simplifying
x = 11