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

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

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

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

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

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

Solving
-12 + -1x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -1x)(4 + -1x) = 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 + -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
Solution
x = {-3, 4}