(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 = 13x
-20 + -1x + x2 = (42 + 13x + x2)

Add '-1x2' to each side of the equation.
-20 + -1x + x2 + -1x2 = 42 + 13x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-20 + -1x + 0 = 42 + 13x + x2 + -1x2
-20 + -1x = 42 + 13x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-20 + -1x = 42 + 13x + 0
-20 + -1x = 42 + 13x

Solving
-20 + -1x = 42 + 13x

Solving for variable 'x'.

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

Add '-13x' to each side of the equation.
-20 + -1x + -13x = 42 + 13x + -13x

Combine like terms: -1x + -13x = -14x
-20 + -14x = 42 + 13x + -13x

Combine like terms: 13x + -13x = 0
-20 + -14x = 42 + 0
-20 + -14x = 42

Add '20' to each side of the equation.
-20 + 20 + -14x = 42 + 20

Combine like terms: -20 + 20 = 0
0 + -14x = 42 + 20
-14x = 42 + 20

Combine like terms: 42 + 20 = 62
-14x = 62

Divide each side by '-14'.
x = -4.428571429

Simplifying
x = -4.428571429