(x-6)(x+4)=24

Solution for (x-6)(x+4)=24 equation:

Simplifying
(x + -6)(x + 4) = 24

Reorder the terms:
(-6 + x)(x + 4) = 24

Reorder the terms:
(-6 + x)(4 + x) = 24

Multiply (-6 + x) * (4 + x)
(-6(4 + x) + x(4 + x)) = 24
((4 * -6 + x * -6) + x(4 + x)) = 24
((-24 + -6x) + x(4 + x)) = 24
(-24 + -6x + (4 * x + x * x)) = 24
(-24 + -6x + (4x + x2)) = 24

Combine like terms: -6x + 4x = -2x
(-24 + -2x + x2) = 24

Solving
-24 + -2x + x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + -24 + -2x + x2 = 24 + -24

Combine like terms: -24 + -24 = -48
-48 + -2x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-48 + -2x + x2 = 0

Factor a trinomial.
(-6 + -1x)(8 + -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 '(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 = {-6, 8}