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

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


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

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

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

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

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

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

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

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

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

Add '-1x2' to each side of the equation.
-3 + 2x + x2 + -1x2 = -6 + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3 + 2x + 0 = -6 + -1x + x2 + -1x2
-3 + 2x = -6 + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3 + 2x = -6 + -1x + 0
-3 + 2x = -6 + -1x

Solving
-3 + 2x = -6 + -1x

Solving for variable 'x'.

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

Add 'x' to each side of the equation.
-3 + 2x + x = -6 + -1x + x

Combine like terms: 2x + x = 3x
-3 + 3x = -6 + -1x + x

Combine like terms: -1x + x = 0
-3 + 3x = -6 + 0
-3 + 3x = -6

Add '3' to each side of the equation.
-3 + 3 + 3x = -6 + 3

Combine like terms: -3 + 3 = 0
0 + 3x = -6 + 3
3x = -6 + 3

Combine like terms: -6 + 3 = -3
3x = -3

Divide each side by '3'.
x = -1

Simplifying
x = -1

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