-3(x-5)(x+6)=0

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Solution for -3(x-5)(x+6)=0 equation:


Simplifying
-3(x + -5)(x + 6) = 0

Reorder the terms:
-3(-5 + x)(x + 6) = 0

Reorder the terms:
-3(-5 + x)(6 + x) = 0

Multiply (-5 + x) * (6 + x)
-3(-5(6 + x) + x(6 + x)) = 0
-3((6 * -5 + x * -5) + x(6 + x)) = 0
-3((-30 + -5x) + x(6 + x)) = 0
-3(-30 + -5x + (6 * x + x * x)) = 0
-3(-30 + -5x + (6x + x2)) = 0

Combine like terms: -5x + 6x = 1x
-3(-30 + 1x + x2) = 0
(-30 * -3 + 1x * -3 + x2 * -3) = 0
(90 + -3x + -3x2) = 0

Solving
90 + -3x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(30 + -1x + -1x2) = 0

Factor a trinomial.
3((5 + -1x)(6 + x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Subproblem 2

Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 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 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6

Solution

x = {5, -6}

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