(6x+2)(x-1)=0

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Solution for (6x+2)(x-1)=0 equation:


Simplifying
(6x + 2)(x + -1) = 0

Reorder the terms:
(2 + 6x)(x + -1) = 0

Reorder the terms:
(2 + 6x)(-1 + x) = 0

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

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

Solving
-2 + -4x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -2x + 3x2) = 0

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

Ignore the factor 2.

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 '(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

Solution

x = {-0.3333333333, 1}

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