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

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


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

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

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

Combine like terms: -4x + 10x = 6x
(-20 + 6x + 2x2) = 0

Solving
-20 + 6x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 3x + x2) = 0

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

Ignore the factor 2.

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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {-5, 2}

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