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

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

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

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

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

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

Combine like terms: 2x + -3x = -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.
(-5 + -1x)(6 + -1x) = 0

Subproblem 1
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
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 = {-5, 6}