2x(x+5)(x+6)=0

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Solution for 2x(x+5)(x+6)=0 equation:


Simplifying
2x(x + 5)(x + 6) = 0

Reorder the terms:
2x(5 + x)(x + 6) = 0

Reorder the terms:
2x(5 + x)(6 + x) = 0

Multiply (5 + x) * (6 + x)
2x(5(6 + x) + x(6 + x)) = 0
2x((6 * 5 + x * 5) + x(6 + x)) = 0
2x((30 + 5x) + x(6 + x)) = 0
2x(30 + 5x + (6 * x + x * x)) = 0
2x(30 + 5x + (6x + x2)) = 0

Combine like terms: 5x + 6x = 11x
2x(30 + 11x + x2) = 0
(30 * 2x + 11x * 2x + x2 * 2x) = 0
(60x + 22x2 + 2x3) = 0

Solving
60x + 22x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(30 + 11x + x2) = 0

Factor a trinomial.
2x((6 + x)(5 + x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

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

Subproblem 3

Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5

Solution

x = {0, -6, -5}

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