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

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


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

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

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

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

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

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

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

Multiply (2 + x) * (-5 + x)
-3 + 2x + x2 = (2(-5 + x) + x(-5 + x))
-3 + 2x + x2 = ((-5 * 2 + x * 2) + x(-5 + x))
-3 + 2x + x2 = ((-10 + 2x) + x(-5 + x))
-3 + 2x + x2 = (-10 + 2x + (-5 * x + x * x))
-3 + 2x + x2 = (-10 + 2x + (-5x + x2))

Combine like terms: 2x + -5x = -3x
-3 + 2x + x2 = (-10 + -3x + x2)

Add '-1x2' to each side of the equation.
-3 + 2x + x2 + -1x2 = -10 + -3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3 + 2x + 0 = -10 + -3x + x2 + -1x2
-3 + 2x = -10 + -3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3 + 2x = -10 + -3x + 0
-3 + 2x = -10 + -3x

Solving
-3 + 2x = -10 + -3x

Solving for variable 'x'.

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

Add '3x' to each side of the equation.
-3 + 2x + 3x = -10 + -3x + 3x

Combine like terms: 2x + 3x = 5x
-3 + 5x = -10 + -3x + 3x

Combine like terms: -3x + 3x = 0
-3 + 5x = -10 + 0
-3 + 5x = -10

Add '3' to each side of the equation.
-3 + 3 + 5x = -10 + 3

Combine like terms: -3 + 3 = 0
0 + 5x = -10 + 3
5x = -10 + 3

Combine like terms: -10 + 3 = -7
5x = -7

Divide each side by '5'.
x = -1.4

Simplifying
x = -1.4

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