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

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

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

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

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

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

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

Reorder the terms:
-2 + 1x + x2 = (3 + x)(x + -3)

Reorder the terms:
-2 + 1x + x2 = (3 + x)(-3 + x)

Multiply (3 + x) * (-3 + x)
-2 + 1x + x2 = (3(-3 + x) + x(-3 + x))
-2 + 1x + x2 = ((-3 * 3 + x * 3) + x(-3 + x))
-2 + 1x + x2 = ((-9 + 3x) + x(-3 + x))
-2 + 1x + x2 = (-9 + 3x + (-3 * x + x * x))
-2 + 1x + x2 = (-9 + 3x + (-3x + x2))

Combine like terms: 3x + -3x = 0
-2 + 1x + x2 = (-9 + 0 + x2)
-2 + 1x + x2 = (-9 + x2)

Add '-1x2' to each side of the equation.
-2 + 1x + x2 + -1x2 = -9 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + 1x + 0 = -9 + x2 + -1x2
-2 + 1x = -9 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + 1x = -9 + 0
-2 + 1x = -9

Solving
-2 + 1x = -9

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + 1x = -9 + 2

Combine like terms: -2 + 2 = 0
0 + 1x = -9 + 2
1x = -9 + 2

Combine like terms: -9 + 2 = -7
1x = -7

Divide each side by '1'.
x = -7

Simplifying
x = -7