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

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


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

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

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

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

Combine like terms: 3x + -4x = -1x
(-2 + -1x + 6x2) = 0

Solving
-2 + -1x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -2x)(2 + -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 '(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 = {-0.5, 0.6666666667}

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