(x-2)(x+6)=48

Solution for (x-2)(x+6)=48 equation:

Simplifying
(x + -2)(x + 6) = 48

Reorder the terms:
(-2 + x)(x + 6) = 48

Reorder the terms:
(-2 + x)(6 + x) = 48

Multiply (-2 + x) * (6 + x)
(-2(6 + x) + x(6 + x)) = 48
((6 * -2 + x * -2) + x(6 + x)) = 48
((-12 + -2x) + x(6 + x)) = 48
(-12 + -2x + (6 * x + x * x)) = 48
(-12 + -2x + (6x + x2)) = 48

Combine like terms: -2x + 6x = 4x
(-12 + 4x + x2) = 48

Solving
-12 + 4x + x2 = 48

Solving for variable 'x'.

Reorder the terms:
-12 + -48 + 4x + x2 = 48 + -48

Combine like terms: -12 + -48 = -60
-60 + 4x + x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-60 + 4x + x2 = 0

Factor a trinomial.
(-10 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10
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 = {-10, 6}