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

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


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

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

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

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

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

Solving
-2 + 5x + 12x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-0.6666666667, 0.25}

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