(x-3)(x+4)=(x-2)(x+2)

Solution for (x-3)(x+4)=(x-2)(x+2) equation:

Simplifying
(x + -3)(x + 4) = (x + -2)(x + 2)

Reorder the terms:
(-3 + x)(x + 4) = (x + -2)(x + 2)

Reorder the terms:
(-3 + x)(4 + x) = (x + -2)(x + 2)

Multiply (-3 + x) * (4 + x)
(-3(4 + x) + x(4 + x)) = (x + -2)(x + 2)
((4 * -3 + x * -3) + x(4 + x)) = (x + -2)(x + 2)
((-12 + -3x) + x(4 + x)) = (x + -2)(x + 2)
(-12 + -3x + (4 * x + x * x)) = (x + -2)(x + 2)
(-12 + -3x + (4x + x2)) = (x + -2)(x + 2)

Combine like terms: -3x + 4x = 1x
(-12 + 1x + x2) = (x + -2)(x + 2)

Reorder the terms:
-12 + 1x + x2 = (-2 + x)(x + 2)

Reorder the terms:
-12 + 1x + x2 = (-2 + x)(2 + x)

Multiply (-2 + x) * (2 + x)
-12 + 1x + x2 = (-2(2 + x) + x(2 + x))
-12 + 1x + x2 = ((2 * -2 + x * -2) + x(2 + x))
-12 + 1x + x2 = ((-4 + -2x) + x(2 + x))
-12 + 1x + x2 = (-4 + -2x + (2 * x + x * x))
-12 + 1x + x2 = (-4 + -2x + (2x + x2))

Combine like terms: -2x + 2x = 0
-12 + 1x + x2 = (-4 + 0 + x2)
-12 + 1x + x2 = (-4 + x2)

Add '-1x2' to each side of the equation.
-12 + 1x + x2 + -1x2 = -4 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + 1x + 0 = -4 + x2 + -1x2
-12 + 1x = -4 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + 1x = -4 + 0
-12 + 1x = -4

Solving
-12 + 1x = -4

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + 1x = -4 + 12

Combine like terms: -12 + 12 = 0
0 + 1x = -4 + 12
1x = -4 + 12

Combine like terms: -4 + 12 = 8
1x = 8

Divide each side by '1'.
x = 8

Simplifying
x = 8