(-x+6)(x+3)=0

Solution for (-x+6)(x+3)=0 equation:

Simplifying
(-1x + 6)(x + 3) = 0

Reorder the terms:
(6 + -1x)(x + 3) = 0

Reorder the terms:
(6 + -1x)(3 + x) = 0

Multiply (6 + -1x) * (3 + x)
(6(3 + x) + -1x * (3 + x)) = 0
((3 * 6 + x * 6) + -1x * (3 + x)) = 0
((18 + 6x) + -1x * (3 + x)) = 0
(18 + 6x + (3 * -1x + x * -1x)) = 0
(18 + 6x + (-3x + -1x2)) = 0

Combine like terms: 6x + -3x = 3x
(18 + 3x + -1x2) = 0

Solving
18 + 3x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6 + -1x)(3 + x) = 0

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
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 = {6, -3}