(x+1)(x+2)=2x^2+22x+20

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Solution for (x+1)(x+2)=2x^2+22x+20 equation: 


Simplifying
(x + 1)(x + 2) = 2x2 + 22x + 20

Reorder the terms:
(1 + x)(x + 2) = 2x2 + 22x + 20

Reorder the terms:
(1 + x)(2 + x) = 2x2 + 22x + 20

Multiply (1 + x) * (2 + x)
(1(2 + x) + x(2 + x)) = 2x2 + 22x + 20
((2 * 1 + x * 1) + x(2 + x)) = 2x2 + 22x + 20
((2 + 1x) + x(2 + x)) = 2x2 + 22x + 20
(2 + 1x + (2 * x + x * x)) = 2x2 + 22x + 20
(2 + 1x + (2x + x2)) = 2x2 + 22x + 20

Combine like terms: 1x + 2x = 3x
(2 + 3x + x2) = 2x2 + 22x + 20

Reorder the terms:
2 + 3x + x2 = 20 + 22x + 2x2

Solving
2 + 3x + x2 = 20 + 22x + 2x2

Solving for variable 'x'.

Reorder the terms:
2 + -20 + 3x + -22x + x2 + -2x2 = 20 + 22x + 2x2 + -20 + -22x + -2x2

Combine like terms: 2 + -20 = -18
-18 + 3x + -22x + x2 + -2x2 = 20 + 22x + 2x2 + -20 + -22x + -2x2

Combine like terms: 3x + -22x = -19x
-18 + -19x + x2 + -2x2 = 20 + 22x + 2x2 + -20 + -22x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-18 + -19x + -1x2 = 20 + 22x + 2x2 + -20 + -22x + -2x2

Reorder the terms:
-18 + -19x + -1x2 = 20 + -20 + 22x + -22x + 2x2 + -2x2

Combine like terms: 20 + -20 = 0
-18 + -19x + -1x2 = 0 + 22x + -22x + 2x2 + -2x2
-18 + -19x + -1x2 = 22x + -22x + 2x2 + -2x2

Combine like terms: 22x + -22x = 0
-18 + -19x + -1x2 = 0 + 2x2 + -2x2
-18 + -19x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-18 + -19x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(18 + 19x + x2) = 0

Factor a trinomial.
-1((18 + x)(1 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(18 + x)' equal to zero and attempt to solve:

Simplifying
18 + x = 0

Solving
18 + x = 0

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

Add '-18' to each side of the equation.
18 + -18 + x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + x = 0 + -18
x = 0 + -18

Combine like terms: 0 + -18 = -18
x = -18

Simplifying
x = -18

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 = {-18, -1}

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