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

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

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

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

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

Solving
12 + -1x + -1x2 = 0

Solving for variable 'x'.

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}