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

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

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

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

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

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

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

Solving
12 + 1x + -1x2 = 0

Solving for variable 'x'.

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}