(8x+48)(4x-4)=0

Solution for (8x+48)(4x-4)=0 equation:

Simplifying
(8x + 48)(4x + -4) = 0

Reorder the terms:
(48 + 8x)(4x + -4) = 0

Reorder the terms:
(48 + 8x)(-4 + 4x) = 0

Multiply (48 + 8x) * (-4 + 4x)
(48(-4 + 4x) + 8x * (-4 + 4x)) = 0
((-4 * 48 + 4x * 48) + 8x * (-4 + 4x)) = 0
((-192 + 192x) + 8x * (-4 + 4x)) = 0
(-192 + 192x + (-4 * 8x + 4x * 8x)) = 0
(-192 + 192x + (-32x + 32x2)) = 0

Combine like terms: 192x + -32x = 160x
(-192 + 160x + 32x2) = 0

Solving
-192 + 160x + 32x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '32'.
32(-6 + 5x + x2) = 0

Factor a trinomial.
32((-6 + -1x)(1 + -1x)) = 0

Ignore the factor 32.
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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-6, 1}