-3(2x-6)(8x+1)=0

Solution for -3(2x-6)(8x+1)=0 equation:

Simplifying
-3(2x + -6)(8x + 1) = 0

Reorder the terms:
-3(-6 + 2x)(8x + 1) = 0

Reorder the terms:
-3(-6 + 2x)(1 + 8x) = 0

Multiply (-6 + 2x) * (1 + 8x)
-3(-6(1 + 8x) + 2x * (1 + 8x)) = 0
-3((1 * -6 + 8x * -6) + 2x * (1 + 8x)) = 0
-3((-6 + -48x) + 2x * (1 + 8x)) = 0
-3(-6 + -48x + (1 * 2x + 8x * 2x)) = 0
-3(-6 + -48x + (2x + 16x2)) = 0

Combine like terms: -48x + 2x = -46x
-3(-6 + -46x + 16x2) = 0
(-6 * -3 + -46x * -3 + 16x2 * -3) = 0
(18 + 138x + -48x2) = 0

Solving
18 + 138x + -48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + 23x + -8x2) = 0

Factor a trinomial.
6((3 + -1x)(1 + 8x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(1 + 8x)' equal to zero and attempt to solve:

Simplifying
1 + 8x = 0

Solving
1 + 8x = 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 + 8x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 8x = 0 + -1
8x = 0 + -1

Combine like terms: 0 + -1 = -1
8x = -1

Divide each side by '8'.
x = -0.125

Simplifying
x = -0.125
Solution
x = {3, -0.125}