(x-9)(x+4)=(x-2)(x+3)

Solution for (x-9)(x+4)=(x-2)(x+3) equation:

Simplifying
(x + -9)(x + 4) = (x + -2)(x + 3)

Reorder the terms:
(-9 + x)(x + 4) = (x + -2)(x + 3)

Reorder the terms:
(-9 + x)(4 + x) = (x + -2)(x + 3)

Multiply (-9 + x) * (4 + x)
(-9(4 + x) + x(4 + x)) = (x + -2)(x + 3)
((4 * -9 + x * -9) + x(4 + x)) = (x + -2)(x + 3)
((-36 + -9x) + x(4 + x)) = (x + -2)(x + 3)
(-36 + -9x + (4 * x + x * x)) = (x + -2)(x + 3)
(-36 + -9x + (4x + x2)) = (x + -2)(x + 3)

Combine like terms: -9x + 4x = -5x
(-36 + -5x + x2) = (x + -2)(x + 3)

Reorder the terms:
-36 + -5x + x2 = (-2 + x)(x + 3)

Reorder the terms:
-36 + -5x + x2 = (-2 + x)(3 + x)

Multiply (-2 + x) * (3 + x)
-36 + -5x + x2 = (-2(3 + x) + x(3 + x))
-36 + -5x + x2 = ((3 * -2 + x * -2) + x(3 + x))
-36 + -5x + x2 = ((-6 + -2x) + x(3 + x))
-36 + -5x + x2 = (-6 + -2x + (3 * x + x * x))
-36 + -5x + x2 = (-6 + -2x + (3x + x2))

Combine like terms: -2x + 3x = 1x
-36 + -5x + x2 = (-6 + 1x + x2)

Add '-1x2' to each side of the equation.
-36 + -5x + x2 + -1x2 = -6 + 1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-36 + -5x + 0 = -6 + 1x + x2 + -1x2
-36 + -5x = -6 + 1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-36 + -5x = -6 + 1x + 0
-36 + -5x = -6 + 1x

Solving
-36 + -5x = -6 + 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.
-36 + -5x + -1x = -6 + 1x + -1x

Combine like terms: -5x + -1x = -6x
-36 + -6x = -6 + 1x + -1x

Combine like terms: 1x + -1x = 0
-36 + -6x = -6 + 0
-36 + -6x = -6

Add '36' to each side of the equation.
-36 + 36 + -6x = -6 + 36

Combine like terms: -36 + 36 = 0
0 + -6x = -6 + 36
-6x = -6 + 36

Combine like terms: -6 + 36 = 30
-6x = 30

Divide each side by '-6'.
x = -5

Simplifying
x = -5