(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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