(x+2)(20+-2x)=40

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Solution for (x+2)(20+-2x)=40 equation: 


Simplifying
(x + 2)(20 + -2x) = 40

Reorder the terms:
(2 + x)(20 + -2x) = 40

Multiply (2 + x) * (20 + -2x)
(2(20 + -2x) + x(20 + -2x)) = 40
((20 * 2 + -2x * 2) + x(20 + -2x)) = 40
((40 + -4x) + x(20 + -2x)) = 40
(40 + -4x + (20 * x + -2x * x)) = 40
(40 + -4x + (20x + -2x2)) = 40

Combine like terms: -4x + 20x = 16x
(40 + 16x + -2x2) = 40

Add '-40' to each side of the equation.
40 + 16x + -40 + -2x2 = 40 + -40

Reorder the terms:
40 + -40 + 16x + -2x2 = 40 + -40

Combine like terms: 40 + -40 = 0
0 + 16x + -2x2 = 40 + -40
16x + -2x2 = 40 + -40

Combine like terms: 40 + -40 = 0
16x + -2x2 = 0

Solving
16x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(8 + -1x) = 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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {0, 8}

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