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

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


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

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

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

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

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

Solving
0 = -12 + -1x + x2

Solving for variable 'x'.

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

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

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

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

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

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


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

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

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