(6+3x)*(-6x+24)=0

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Solution for (6+3x)*(-6x+24)=0 equation:


Simplifying
(6 + 3x)(-6x + 24) = 0

Reorder the terms:
(6 + 3x)(24 + -6x) = 0

Multiply (6 + 3x) * (24 + -6x)
(6(24 + -6x) + 3x * (24 + -6x)) = 0
((24 * 6 + -6x * 6) + 3x * (24 + -6x)) = 0
((144 + -36x) + 3x * (24 + -6x)) = 0
(144 + -36x + (24 * 3x + -6x * 3x)) = 0
(144 + -36x + (72x + -18x2)) = 0

Combine like terms: -36x + 72x = 36x
(144 + 36x + -18x2) = 0

Solving
144 + 36x + -18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '18'.
18(8 + 2x + -1x2) = 0

Factor a trinomial.
18((4 + -1x)(2 + x)) = 0

Ignore the factor 18.

Subproblem 1

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Subproblem 2

Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Solution

x = {4, -2}

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