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

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


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

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

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

Multiply (-4 + 3x) * (1 + 2x)
(-4(1 + 2x) + 3x * (1 + 2x)) = 0
((1 * -4 + 2x * -4) + 3x * (1 + 2x)) = 0
((-4 + -8x) + 3x * (1 + 2x)) = 0
(-4 + -8x + (1 * 3x + 2x * 3x)) = 0
(-4 + -8x + (3x + 6x2)) = 0

Combine like terms: -8x + 3x = -5x
(-4 + -5x + 6x2) = 0

Solving
-4 + -5x + 6x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5

Subproblem 2

Set the factor '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333

Solution

x = {-0.5, 1.333333333}

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