2(x+4)(3x-1)=0

Solution for 2(x+4)(3x-1)=0 equation:

Simplifying
2(x + 4)(3x + -1) = 0

Reorder the terms:
2(4 + x)(3x + -1) = 0

Reorder the terms:
2(4 + x)(-1 + 3x) = 0

Multiply (4 + x) * (-1 + 3x)
2(4(-1 + 3x) + x(-1 + 3x)) = 0
2((-1 * 4 + 3x * 4) + x(-1 + 3x)) = 0
2((-4 + 12x) + x(-1 + 3x)) = 0
2(-4 + 12x + (-1 * x + 3x * x)) = 0
2(-4 + 12x + (-1x + 3x2)) = 0

Combine like terms: 12x + -1x = 11x
2(-4 + 11x + 3x2) = 0
(-4 * 2 + 11x * 2 + 3x2 * 2) = 0
(-8 + 22x + 6x2) = 0

Solving
-8 + 22x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 11x + 3x2) = 0

Factor a trinomial.
2((-4 + -1x)(1 + -3x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-4, 0.3333333333}