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

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

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

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

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

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

Combine like terms: -2x + 9x = 7x
(-18 + 7x + x2) = 10x

Solving
-18 + 7x + x2 = 10x

Solving for variable 'x'.

Reorder the terms:
-18 + 7x + -10x + x2 = 10x + -10x

Combine like terms: 7x + -10x = -3x
-18 + -3x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-18 + -3x + x2 = 0

Factor a trinomial.
(-3 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
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 = {-3, 6}