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

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

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

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

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

Multiply (4 + 2x) * (-1 + 3x)
0 = (4(-1 + 3x) + 2x * (-1 + 3x))
0 = ((-1 * 4 + 3x * 4) + 2x * (-1 + 3x))
0 = ((-4 + 12x) + 2x * (-1 + 3x))
0 = (-4 + 12x + (-1 * 2x + 3x * 2x))
0 = (-4 + 12x + (-2x + 6x2))

Combine like terms: 12x + -2x = 10x
0 = (-4 + 10x + 6x2)

Solving
0 = -4 + 10x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + 4 = 4
4 + -10x + -6x2 = -4 + 10x + 6x2 + 4 + -10x + -6x2

Reorder the terms:
4 + -10x + -6x2 = -4 + 4 + 10x + -10x + 6x2 + -6x2

Combine like terms: -4 + 4 = 0
4 + -10x + -6x2 = 0 + 10x + -10x + 6x2 + -6x2
4 + -10x + -6x2 = 10x + -10x + 6x2 + -6x2

Combine like terms: 10x + -10x = 0
4 + -10x + -6x2 = 0 + 6x2 + -6x2
4 + -10x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
4 + -10x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -5x + -3x2) = 0

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

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {0.3333333333, -2}