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

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


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