(x-3)(x-2)=9x+21

Solution for (x-3)(x-2)=9x+21 equation:

Simplifying
(x + -3)(x + -2) = 9x + 21

Reorder the terms:
(-3 + x)(x + -2) = 9x + 21

Reorder the terms:
(-3 + x)(-2 + x) = 9x + 21

Multiply (-3 + x) * (-2 + x)
(-3(-2 + x) + x(-2 + x)) = 9x + 21
((-2 * -3 + x * -3) + x(-2 + x)) = 9x + 21
((6 + -3x) + x(-2 + x)) = 9x + 21
(6 + -3x + (-2 * x + x * x)) = 9x + 21
(6 + -3x + (-2x + x2)) = 9x + 21

Combine like terms: -3x + -2x = -5x
(6 + -5x + x2) = 9x + 21

Reorder the terms:
6 + -5x + x2 = 21 + 9x

Solving
6 + -5x + x2 = 21 + 9x

Solving for variable 'x'.

Reorder the terms:
6 + -21 + -5x + -9x + x2 = 21 + 9x + -21 + -9x

Combine like terms: 6 + -21 = -15
-15 + -5x + -9x + x2 = 21 + 9x + -21 + -9x

Combine like terms: -5x + -9x = -14x
-15 + -14x + x2 = 21 + 9x + -21 + -9x

Reorder the terms:
-15 + -14x + x2 = 21 + -21 + 9x + -9x

Combine like terms: 21 + -21 = 0
-15 + -14x + x2 = 0 + 9x + -9x
-15 + -14x + x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-15 + -14x + x2 = 0

Factor a trinomial.
(-1 + -1x)(15 + -1x) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {-1, 15}