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

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

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

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

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

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

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

Solving
0 = -12 + 1x + x2

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(3 + -1x)(4 + x) = 0

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

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

Simplifying
x = 3
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

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

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

Simplifying
x = -4
Solution
x = {3, -4}