(x-9)(5x+12)=0

Solution for (x-9)(5x+12)=0 equation:

Simplifying
(x + -9)(5x + 12) = 0

Reorder the terms:
(-9 + x)(5x + 12) = 0

Reorder the terms:
(-9 + x)(12 + 5x) = 0

Multiply (-9 + x) * (12 + 5x)
(-9(12 + 5x) + x(12 + 5x)) = 0
((12 * -9 + 5x * -9) + x(12 + 5x)) = 0
((-108 + -45x) + x(12 + 5x)) = 0
(-108 + -45x + (12 * x + 5x * x)) = 0
(-108 + -45x + (12x + 5x2)) = 0

Combine like terms: -45x + 12x = -33x
(-108 + -33x + 5x2) = 0

Solving
-108 + -33x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-12 + -5x)(9 + -1x) = 0

Subproblem 1
Set the factor '(-12 + -5x)' equal to zero and attempt to solve:

Simplifying
-12 + -5x = 0

Solving
-12 + -5x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -5x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -5x = 0 + 12
-5x = 0 + 12

Combine like terms: 0 + 12 = 12
-5x = 12

Divide each side by '-5'.
x = -2.4

Simplifying
x = -2.4
Subproblem 2
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
Solution
x = {-2.4, 9}