-5(x+9)(-x+6)=0

Solution for -5(x+9)(-x+6)=0 equation:

Simplifying
-5(x + 9)(-1x + 6) = 0

Reorder the terms:
-5(9 + x)(-1x + 6) = 0

Reorder the terms:
-5(9 + x)(6 + -1x) = 0

Multiply (9 + x) * (6 + -1x)
-5(9(6 + -1x) + x(6 + -1x)) = 0
-5((6 * 9 + -1x * 9) + x(6 + -1x)) = 0
-5((54 + -9x) + x(6 + -1x)) = 0
-5(54 + -9x + (6 * x + -1x * x)) = 0
-5(54 + -9x + (6x + -1x2)) = 0

Combine like terms: -9x + 6x = -3x
-5(54 + -3x + -1x2) = 0
(54 * -5 + -3x * -5 + -1x2 * -5) = 0
(-270 + 15x + 5x2) = 0

Solving
-270 + 15x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-54 + 3x + x2) = 0

Factor a trinomial.
5((-9 + -1x)(6 + -1x)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
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
Solution
x = {-9, 6}