(x-2)(x+3)=(x-1)(x-5)

Solution for (x-2)(x+3)=(x-1)(x-5) equation:

Simplifying
(x + -2)(x + 3) = (x + -1)(x + -5)

Reorder the terms:
(-2 + x)(x + 3) = (x + -1)(x + -5)

Reorder the terms:
(-2 + x)(3 + x) = (x + -1)(x + -5)

Multiply (-2 + x) * (3 + x)
(-2(3 + x) + x(3 + x)) = (x + -1)(x + -5)
((3 * -2 + x * -2) + x(3 + x)) = (x + -1)(x + -5)
((-6 + -2x) + x(3 + x)) = (x + -1)(x + -5)
(-6 + -2x + (3 * x + x * x)) = (x + -1)(x + -5)
(-6 + -2x + (3x + x2)) = (x + -1)(x + -5)

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

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

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

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

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

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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

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

Combine like terms: 5 + 6 = 11
7x = 11

Divide each side by '7'.
x = 1.571428571

Simplifying
x = 1.571428571