(3x+6)(4x-8)=0

Solution for (3x+6)(4x-8)=0 equation:

Simplifying
(3x + 6)(4x + -8) = 0

Reorder the terms:
(6 + 3x)(4x + -8) = 0

Reorder the terms:
(6 + 3x)(-8 + 4x) = 0

Multiply (6 + 3x) * (-8 + 4x)
(6(-8 + 4x) + 3x * (-8 + 4x)) = 0
((-8 * 6 + 4x * 6) + 3x * (-8 + 4x)) = 0
((-48 + 24x) + 3x * (-8 + 4x)) = 0
(-48 + 24x + (-8 * 3x + 4x * 3x)) = 0
(-48 + 24x + (-24x + 12x2)) = 0

Combine like terms: 24x + -24x = 0
(-48 + 0 + 12x2) = 0
(-48 + 12x2) = 0

Solving
-48 + 12x2 = 0

Solving for variable 'x'.

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

Add '48' to each side of the equation.
-48 + 48 + 12x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 12x2 = 0 + 48
12x2 = 0 + 48

Combine like terms: 0 + 48 = 48
12x2 = 48

Divide each side by '12'.
x2 = 4

Simplifying
x2 = 4

Take the square root of each side:
x = {-2, 2}