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

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


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

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

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

Combine like terms: 1x + 6x = 7x
(-2 + 7x + -3x2) = 0

Solving
-2 + 7x + -3x2 = 0

Solving for variable 'x'.

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

Subproblem 1

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

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 = {2, 0.3333333333}

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