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

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


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

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

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

Multiply (1 + 6x) * (-6 + 2x)
(1(-6 + 2x) + 6x * (-6 + 2x)) = 0
((-6 * 1 + 2x * 1) + 6x * (-6 + 2x)) = 0
((-6 + 2x) + 6x * (-6 + 2x)) = 0
(-6 + 2x + (-6 * 6x + 2x * 6x)) = 0
(-6 + 2x + (-36x + 12x2)) = 0

Combine like terms: 2x + -36x = -34x
(-6 + -34x + 12x2) = 0

Solving
-6 + -34x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -17x + 6x2) = 0

Factor a trinomial.
2((-1 + -6x)(3 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + -6x)' equal to zero and attempt to solve: Simplifying -1 + -6x = 0 Solving -1 + -6x = 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 + -6x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6x = 0 + 1 -6x = 0 + 1 Combine like terms: 0 + 1 = 1 -6x = 1 Divide each side by '-6'. x = -0.1666666667 Simplifying x = -0.1666666667

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {-0.1666666667, 3}

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