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

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


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

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

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

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

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

Solving
-1 + 2x + 3x2 = 0

Solving for variable 'x'.

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

Subproblem 1

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

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 = {-1, 0.3333333333}

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