(4+x)(20-2x)=0

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Solution for (4+x)(20-2x)=0 equation:


Simplifying
(4 + x)(20 + -2x) = 0

Multiply (4 + x) * (20 + -2x)
(4(20 + -2x) + x(20 + -2x)) = 0
((20 * 4 + -2x * 4) + x(20 + -2x)) = 0
((80 + -8x) + x(20 + -2x)) = 0
(80 + -8x + (20 * x + -2x * x)) = 0
(80 + -8x + (20x + -2x2)) = 0

Combine like terms: -8x + 20x = 12x
(80 + 12x + -2x2) = 0

Solving
80 + 12x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(40 + 6x + -1x2) = 0

Factor a trinomial.
2((10 + -1x)(4 + x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10

Subproblem 2

Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Solution

x = {10, -4}

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