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

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

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

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

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

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

Combine like terms: -2x + -9x = -11x
(18 + -11x + x2) = -10

Solving
18 + -11x + x2 = -10

Solving for variable 'x'.

Reorder the terms:
18 + 10 + -11x + x2 = -10 + 10

Combine like terms: 18 + 10 = 28
28 + -11x + x2 = -10 + 10

Combine like terms: -10 + 10 = 0
28 + -11x + x2 = 0

Factor a trinomial.
(4 + -1x)(7 + -1x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {4, 7}