5(x+2)=(x+1)(x+2)

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Solution for 5(x+2)=(x+1)(x+2) equation: 


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

Reorder the terms:
5(2 + x) = (x + 1)(x + 2)
(2 * 5 + x * 5) = (x + 1)(x + 2)
(10 + 5x) = (x + 1)(x + 2)

Reorder the terms:
10 + 5x = (1 + x)(x + 2)

Reorder the terms:
10 + 5x = (1 + x)(2 + x)

Multiply (1 + x) * (2 + x)
10 + 5x = (1(2 + x) + x(2 + x))
10 + 5x = ((2 * 1 + x * 1) + x(2 + x))
10 + 5x = ((2 + 1x) + x(2 + x))
10 + 5x = (2 + 1x + (2 * x + x * x))
10 + 5x = (2 + 1x + (2x + x2))

Combine like terms: 1x + 2x = 3x
10 + 5x = (2 + 3x + x2)

Solving
10 + 5x = 2 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
10 + -2 + 5x + -3x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Combine like terms: 10 + -2 = 8
8 + 5x + -3x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Combine like terms: 5x + -3x = 2x
8 + 2x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Reorder the terms:
8 + 2x + -1x2 = 2 + -2 + 3x + -3x + x2 + -1x2

Combine like terms: 2 + -2 = 0
8 + 2x + -1x2 = 0 + 3x + -3x + x2 + -1x2
8 + 2x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
8 + 2x + -1x2 = 0 + x2 + -1x2
8 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + 2x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(2 + x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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 = {4, -2}

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