20(x+2)=(x+1)(x+2)

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Solution for 20(x+2)=(x+1)(x+2) equation: 


Simplifying
20(x + 2) = (x + 1)(x + 2)

Reorder the terms:
20(2 + x) = (x + 1)(x + 2)
(2 * 20 + x * 20) = (x + 1)(x + 2)
(40 + 20x) = (x + 1)(x + 2)

Reorder the terms:
40 + 20x = (1 + x)(x + 2)

Reorder the terms:
40 + 20x = (1 + x)(2 + x)

Multiply (1 + x) * (2 + x)
40 + 20x = (1(2 + x) + x(2 + x))
40 + 20x = ((2 * 1 + x * 1) + x(2 + x))
40 + 20x = ((2 + 1x) + x(2 + x))
40 + 20x = (2 + 1x + (2 * x + x * x))
40 + 20x = (2 + 1x + (2x + x2))

Combine like terms: 1x + 2x = 3x
40 + 20x = (2 + 3x + x2)

Solving
40 + 20x = 2 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
40 + -2 + 20x + -3x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Combine like terms: 40 + -2 = 38
38 + 20x + -3x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Combine like terms: 20x + -3x = 17x
38 + 17x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Reorder the terms:
38 + 17x + -1x2 = 2 + -2 + 3x + -3x + x2 + -1x2

Combine like terms: 2 + -2 = 0
38 + 17x + -1x2 = 0 + 3x + -3x + x2 + -1x2
38 + 17x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
38 + 17x + -1x2 = 0 + x2 + -1x2
38 + 17x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
38 + 17x + -1x2 = 0

Factor a trinomial.
(19 + -1x)(2 + x) = 0


Subproblem 1
Set the factor '(19 + -1x)' equal to zero and attempt to solve:

Simplifying
19 + -1x = 0

Solving
19 + -1x = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1x = 0 + -19
-1x = 0 + -19

Combine like terms: 0 + -19 = -19
-1x = -19

Divide each side by '-1'.
x = 19

Simplifying
x = 19

Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {19, -2}

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