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

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


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

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

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

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

Combine like terms: -12x + 1x = -11x
6(-6 + -11x + 2x2) = 0
(-6 * 6 + -11x * 6 + 2x2 * 6) = 0
(-36 + -66x + 12x2) = 0

Solving
-36 + -66x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-6 + -11x + 2x2) = 0

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

Ignore the factor 6.

Subproblem 1

Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {-0.5, 6}

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