(x-2)(x-3)=30

Solution for (x-2)(x-3)=30 equation:

Simplifying
(x + -2)(x + -3) = 30

Reorder the terms:
(-2 + x)(x + -3) = 30

Reorder the terms:
(-2 + x)(-3 + x) = 30

Multiply (-2 + x) * (-3 + x)
(-2(-3 + x) + x(-3 + x)) = 30
((-3 * -2 + x * -2) + x(-3 + x)) = 30
((6 + -2x) + x(-3 + x)) = 30
(6 + -2x + (-3 * x + x * x)) = 30
(6 + -2x + (-3x + x2)) = 30

Combine like terms: -2x + -3x = -5x
(6 + -5x + x2) = 30

Solving
6 + -5x + x2 = 30

Solving for variable 'x'.

Reorder the terms:
6 + -30 + -5x + x2 = 30 + -30

Combine like terms: 6 + -30 = -24
-24 + -5x + x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-24 + -5x + x2 = 0

Factor a trinomial.
(-3 + -1x)(8 + -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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-3, 8}