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

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


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

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

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

Multiply (2 + 3x) * (-1 + 4x)
0 = (2(-1 + 4x) + 3x * (-1 + 4x))
0 = ((-1 * 2 + 4x * 2) + 3x * (-1 + 4x))
0 = ((-2 + 8x) + 3x * (-1 + 4x))
0 = (-2 + 8x + (-1 * 3x + 4x * 3x))
0 = (-2 + 8x + (-3x + 12x2))

Combine like terms: 8x + -3x = 5x
0 = (-2 + 5x + 12x2)

Solving
0 = -2 + 5x + 12x2

Solving for variable 'x'.

Combine like terms: 0 + 2 = 2
2 + -5x + -12x2 = -2 + 5x + 12x2 + 2 + -5x + -12x2

Reorder the terms:
2 + -5x + -12x2 = -2 + 2 + 5x + -5x + 12x2 + -12x2

Combine like terms: -2 + 2 = 0
2 + -5x + -12x2 = 0 + 5x + -5x + 12x2 + -12x2
2 + -5x + -12x2 = 5x + -5x + 12x2 + -12x2

Combine like terms: 5x + -5x = 0
2 + -5x + -12x2 = 0 + 12x2 + -12x2
2 + -5x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
2 + -5x + -12x2 = 0

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


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

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

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

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

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

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

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {0.25, -0.6666666667}

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