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

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

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

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

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

Multiply (2 + x) * (-3 + x)
(2(-3 + x) + x(-3 + x)) = (x + 9)(x + -4)
((-3 * 2 + x * 2) + x(-3 + x)) = (x + 9)(x + -4)
((-6 + 2x) + x(-3 + x)) = (x + 9)(x + -4)
(-6 + 2x + (-3 * x + x * x)) = (x + 9)(x + -4)
(-6 + 2x + (-3x + x2)) = (x + 9)(x + -4)

Combine like terms: 2x + -3x = -1x
(-6 + -1x + x2) = (x + 9)(x + -4)

Reorder the terms:
-6 + -1x + x2 = (9 + x)(x + -4)

Reorder the terms:
-6 + -1x + x2 = (9 + x)(-4 + x)

Multiply (9 + x) * (-4 + x)
-6 + -1x + x2 = (9(-4 + x) + x(-4 + x))
-6 + -1x + x2 = ((-4 * 9 + x * 9) + x(-4 + x))
-6 + -1x + x2 = ((-36 + 9x) + x(-4 + x))
-6 + -1x + x2 = (-36 + 9x + (-4 * x + x * x))
-6 + -1x + x2 = (-36 + 9x + (-4x + x2))

Combine like terms: 9x + -4x = 5x
-6 + -1x + x2 = (-36 + 5x + x2)

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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

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

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

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

Simplifying
x = 5