2(x+1)(x+5)=0

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Solution for 2(x+1)(x+5)=0 equation:


Simplifying
2(x + 1)(x + 5) = 0

Reorder the terms:
2(1 + x)(x + 5) = 0

Reorder the terms:
2(1 + x)(5 + x) = 0

Multiply (1 + x) * (5 + x)
2(1(5 + x) + x(5 + x)) = 0
2((5 * 1 + x * 1) + x(5 + x)) = 0
2((5 + 1x) + x(5 + x)) = 0
2(5 + 1x + (5 * x + x * x)) = 0
2(5 + 1x + (5x + x2)) = 0

Combine like terms: 1x + 5x = 6x
2(5 + 6x + x2) = 0
(5 * 2 + 6x * 2 + x2 * 2) = 0
(10 + 12x + 2x2) = 0

Solving
10 + 12x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 6x + x2) = 0

Factor a trinomial.
2((5 + x)(1 + x)) = 0

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {-5, -1}

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