(x-3)-(x-3)(x+4)=0

Solution for (x-3)-(x-3)(x+4)=0 equation:

Simplifying
(x + -3) + -1(x + -3)(x + 4) = 0

Reorder the terms:
(-3 + x) + -1(x + -3)(x + 4) = 0

Remove parenthesis around (-3 + x)
-3 + x + -1(x + -3)(x + 4) = 0

Reorder the terms:
-3 + x + -1(-3 + x)(x + 4) = 0

Reorder the terms:
-3 + x + -1(-3 + x)(4 + x) = 0

Multiply (-3 + x) * (4 + x)
-3 + x + -1(-3(4 + x) + x(4 + x)) = 0
-3 + x + -1((4 * -3 + x * -3) + x(4 + x)) = 0
-3 + x + -1((-12 + -3x) + x(4 + x)) = 0
-3 + x + -1(-12 + -3x + (4 * x + x * x)) = 0
-3 + x + -1(-12 + -3x + (4x + x2)) = 0

Combine like terms: -3x + 4x = 1x
-3 + x + -1(-12 + 1x + x2) = 0
-3 + x + (-12 * -1 + 1x * -1 + x2 * -1) = 0
-3 + x + (12 + -1x + -1x2) = 0

Reorder the terms:
-3 + 12 + x + -1x + -1x2 = 0

Combine like terms: -3 + 12 = 9
9 + x + -1x + -1x2 = 0

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

Solving
9 + -1x2 = 0

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + -1x2 = 0 + -9

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

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

Divide each side by '-1'.
x2 = 9

Simplifying
x2 = 9

Take the square root of each side:
x = {-3, 3}