(x+2)(x-3)=(x-5)(x-6)

Solution for (x+2)(x-3)=(x-5)(x-6) equation:

Simplifying
(x + 2)(x + -3) = (x + -5)(x + -6)

Reorder the terms:
(2 + x)(x + -3) = (x + -5)(x + -6)

Reorder the terms:
(2 + x)(-3 + x) = (x + -5)(x + -6)

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

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

Reorder the terms:
-6 + -1x + x2 = (-5 + x)(x + -6)

Reorder the terms:
-6 + -1x + x2 = (-5 + x)(-6 + x)

Multiply (-5 + x) * (-6 + x)
-6 + -1x + x2 = (-5(-6 + x) + x(-6 + x))
-6 + -1x + x2 = ((-6 * -5 + x * -5) + x(-6 + x))
-6 + -1x + x2 = ((30 + -5x) + x(-6 + x))
-6 + -1x + x2 = (30 + -5x + (-6 * x + x * x))
-6 + -1x + x2 = (30 + -5x + (-6x + x2))

Combine like terms: -5x + -6x = -11x
-6 + -1x + x2 = (30 + -11x + x2)

Add '-1x2' to each side of the equation.
-6 + -1x + x2 + -1x2 = 30 + -11x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + -1x + 0 = 30 + -11x + x2 + -1x2
-6 + -1x = 30 + -11x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + -1x = 30 + -11x + 0
-6 + -1x = 30 + -11x

Solving
-6 + -1x = 30 + -11x

Solving for variable 'x'.

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

Add '11x' to each side of the equation.
-6 + -1x + 11x = 30 + -11x + 11x

Combine like terms: -1x + 11x = 10x
-6 + 10x = 30 + -11x + 11x

Combine like terms: -11x + 11x = 0
-6 + 10x = 30 + 0
-6 + 10x = 30

Add '6' to each side of the equation.
-6 + 6 + 10x = 30 + 6

Combine like terms: -6 + 6 = 0
0 + 10x = 30 + 6
10x = 30 + 6

Combine like terms: 30 + 6 = 36
10x = 36

Divide each side by '10'.
x = 3.6

Simplifying
x = 3.6