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

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


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

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

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

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

Combine like terms: 1x + -6x = -5x
(-2 + -5x + 3x2) = 0

Solving
-2 + -5x + 3x2 = 0

Solving for variable 'x'.

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

Subproblem 1

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

Subproblem 2

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

Solution

x = {-0.3333333333, 2}

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