(2x-12)(9x+10)=0

Solution for (2x-12)(9x+10)=0 equation:

Simplifying
(2x + -12)(9x + 10) = 0

Reorder the terms:
(-12 + 2x)(9x + 10) = 0

Reorder the terms:
(-12 + 2x)(10 + 9x) = 0

Multiply (-12 + 2x) * (10 + 9x)
(-12(10 + 9x) + 2x * (10 + 9x)) = 0
((10 * -12 + 9x * -12) + 2x * (10 + 9x)) = 0
((-120 + -108x) + 2x * (10 + 9x)) = 0
(-120 + -108x + (10 * 2x + 9x * 2x)) = 0
(-120 + -108x + (20x + 18x2)) = 0

Combine like terms: -108x + 20x = -88x
(-120 + -88x + 18x2) = 0

Solving
-120 + -88x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-60 + -44x + 9x2) = 0

Factor a trinomial.
2((-10 + -9x)(6 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10 + -9x)' equal to zero and attempt to solve:

Simplifying
-10 + -9x = 0

Solving
-10 + -9x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -9x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -9x = 0 + 10
-9x = 0 + 10

Combine like terms: 0 + 10 = 10
-9x = 10

Divide each side by '-9'.
x = -1.111111111

Simplifying
x = -1.111111111
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 = {-1.111111111, 6}