10(x+2)=(x+1)(x+2)

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Solution for 10(x+2)=(x+1)(x+2) equation: 


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

Reorder the terms:
10(2 + x) = (x + 1)(x + 2)
(2 * 10 + x * 10) = (x + 1)(x + 2)
(20 + 10x) = (x + 1)(x + 2)

Reorder the terms:
20 + 10x = (1 + x)(x + 2)

Reorder the terms:
20 + 10x = (1 + x)(2 + x)

Multiply (1 + x) * (2 + x)
20 + 10x = (1(2 + x) + x(2 + x))
20 + 10x = ((2 * 1 + x * 1) + x(2 + x))
20 + 10x = ((2 + 1x) + x(2 + x))
20 + 10x = (2 + 1x + (2 * x + x * x))
20 + 10x = (2 + 1x + (2x + x2))

Combine like terms: 1x + 2x = 3x
20 + 10x = (2 + 3x + x2)

Solving
20 + 10x = 2 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
20 + -2 + 10x + -3x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Combine like terms: 20 + -2 = 18
18 + 10x + -3x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Combine like terms: 10x + -3x = 7x
18 + 7x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Reorder the terms:
18 + 7x + -1x2 = 2 + -2 + 3x + -3x + x2 + -1x2

Combine like terms: 2 + -2 = 0
18 + 7x + -1x2 = 0 + 3x + -3x + x2 + -1x2
18 + 7x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
18 + 7x + -1x2 = 0 + x2 + -1x2
18 + 7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
18 + 7x + -1x2 = 0

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


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 '(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 = {9, -2}

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