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

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

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

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

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

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

Combine like terms: -10x + 9x = -1x
(-90 + -1x + x2) = 0

Solving
-90 + -1x + x2 = 0

Solving for variable 'x'.

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

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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 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 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-9, 10}