(4x+2)(5+x)=0

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Solution for (4x+2)(5+x)=0 equation:


Simplifying
(4x + 2)(5 + x) = 0

Reorder the terms:
(2 + 4x)(5 + x) = 0

Multiply (2 + 4x) * (5 + x)
(2(5 + x) + 4x * (5 + x)) = 0
((5 * 2 + x * 2) + 4x * (5 + x)) = 0
((10 + 2x) + 4x * (5 + x)) = 0
(10 + 2x + (5 * 4x + x * 4x)) = 0
(10 + 2x + (20x + 4x2)) = 0

Combine like terms: 2x + 20x = 22x
(10 + 22x + 4x2) = 0

Solving
10 + 22x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 11x + 2x2) = 0

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

Solution

x = {-5, -0.5}

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