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

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


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

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

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

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

Combine like terms: 3x + -2x = 1x
(-1 + 1x + 6x2) = 0

Solving
-1 + 1x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -2x)(1 + -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 '(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

Solution

x = {-0.5, 0.3333333333}

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