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

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

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

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

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

Multiply (-9 + x) * (10 + 2x)
(-9(10 + 2x) + x(10 + 2x)) = 0
((10 * -9 + 2x * -9) + x(10 + 2x)) = 0
((-90 + -18x) + x(10 + 2x)) = 0
(-90 + -18x + (10 * x + 2x * x)) = 0
(-90 + -18x + (10x + 2x2)) = 0

Combine like terms: -18x + 10x = -8x
(-90 + -8x + 2x2) = 0

Solving
-90 + -8x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + -4x + x2) = 0

Factor a trinomial.
2((-5 + -1x)(9 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
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 = {-5, 9}