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

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


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

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

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

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

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

Add '1' to each side of the equation.
-1 + 2x + 1 + 3x2 = -1 + 1

Reorder the terms:
-1 + 1 + 2x + 3x2 = -1 + 1

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

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

Solving
2x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(2 + 3x) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

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, -0.6666666667}

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