(x-3)(x-2)=(x+2)(x+5)

Solution for (x-3)(x-2)=(x+2)(x+5) equation:

Simplifying
(x + -3)(x + -2) = (x + 2)(x + 5)

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

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

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

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

Reorder the terms:
6 + -5x + x2 = (2 + x)(x + 5)

Reorder the terms:
6 + -5x + x2 = (2 + x)(5 + x)

Multiply (2 + x) * (5 + x)
6 + -5x + x2 = (2(5 + x) + x(5 + x))
6 + -5x + x2 = ((5 * 2 + x * 2) + x(5 + x))
6 + -5x + x2 = ((10 + 2x) + x(5 + x))
6 + -5x + x2 = (10 + 2x + (5 * x + x * x))
6 + -5x + x2 = (10 + 2x + (5x + x2))

Combine like terms: 2x + 5x = 7x
6 + -5x + x2 = (10 + 7x + x2)

Add '-1x2' to each side of the equation.
6 + -5x + x2 + -1x2 = 10 + 7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + -5x + 0 = 10 + 7x + x2 + -1x2
6 + -5x = 10 + 7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + -5x = 10 + 7x + 0
6 + -5x = 10 + 7x

Solving
6 + -5x = 10 + 7x

Solving for variable 'x'.

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

Add '-7x' to each side of the equation.
6 + -5x + -7x = 10 + 7x + -7x

Combine like terms: -5x + -7x = -12x
6 + -12x = 10 + 7x + -7x

Combine like terms: 7x + -7x = 0
6 + -12x = 10 + 0
6 + -12x = 10

Add '-6' to each side of the equation.
6 + -6 + -12x = 10 + -6

Combine like terms: 6 + -6 = 0
0 + -12x = 10 + -6
-12x = 10 + -6

Combine like terms: 10 + -6 = 4
-12x = 4

Divide each side by '-12'.
x = -0.3333333333

Simplifying
x = -0.3333333333