(x+3)*(x-2)=24

Solution for (x+3)*(x-2)=24 equation:

Simplifying
(x + 3)(x + -2) = 24

Reorder the terms:
(3 + x)(x + -2) = 24

Reorder the terms:
(3 + x)(-2 + x) = 24

Multiply (3 + x) * (-2 + x)
(3(-2 + x) + x(-2 + x)) = 24
((-2 * 3 + x * 3) + x(-2 + x)) = 24
((-6 + 3x) + x(-2 + x)) = 24
(-6 + 3x + (-2 * x + x * x)) = 24
(-6 + 3x + (-2x + x2)) = 24

Combine like terms: 3x + -2x = 1x
(-6 + 1x + x2) = 24

Solving
-6 + 1x + x2 = 24

Solving for variable 'x'.

Reorder the terms:
-6 + -24 + 1x + x2 = 24 + -24

Combine like terms: -6 + -24 = -30
-30 + 1x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-30 + 1x + x2 = 0

Factor a trinomial.
(-6 + -1x)(5 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-6, 5}