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

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


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

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

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

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

Combine like terms: 4x + -3x = 1x
(-1 + 1x + 12x2) = 0

Solving
-1 + 1x + 12x2 = 0

Solving for variable 'x'.

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


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 '(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 = {-0.3333333333, 0.25}

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