(x+2)(20-2x)=22

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Solution for (x+2)(20-2x)=22 equation: 


Simplifying
(x + 2)(20 + -2x) = 22

Reorder the terms:
(2 + x)(20 + -2x) = 22

Multiply (2 + x) * (20 + -2x)
(2(20 + -2x) + x(20 + -2x)) = 22
((20 * 2 + -2x * 2) + x(20 + -2x)) = 22
((40 + -4x) + x(20 + -2x)) = 22
(40 + -4x + (20 * x + -2x * x)) = 22
(40 + -4x + (20x + -2x2)) = 22

Combine like terms: -4x + 20x = 16x
(40 + 16x + -2x2) = 22

Solving
40 + 16x + -2x2 = 22

Solving for variable 'x'.

Reorder the terms:
40 + -22 + 16x + -2x2 = 22 + -22

Combine like terms: 40 + -22 = 18
18 + 16x + -2x2 = 22 + -22

Combine like terms: 22 + -22 = 0
18 + 16x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 8x + -1x2) = 0

Factor a trinomial.
2((9 + -1x)(1 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9

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 = {9, -1}

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