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

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

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

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

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

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

Combine like terms: 10x + -18x = -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}