6x=(x+2)(x+1)

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Solution for 6x=(x+2)(x+1) equation: 


Simplifying
6x = (x + 2)(x + 1)

Reorder the terms:
6x = (2 + x)(x + 1)

Reorder the terms:
6x = (2 + x)(1 + x)

Multiply (2 + x) * (1 + x)
6x = (2(1 + x) + x(1 + x))
6x = ((1 * 2 + x * 2) + x(1 + x))
6x = ((2 + 2x) + x(1 + x))
6x = (2 + 2x + (1 * x + x * x))
6x = (2 + 2x + (1x + x2))

Combine like terms: 2x + 1x = 3x
6x = (2 + 3x + x2)

Solving
6x = 2 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
-2 + 6x + -3x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Combine like terms: 6x + -3x = 3x
-2 + 3x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

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

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

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

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

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


Subproblem 1
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

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
Solution
x = {2, 1}

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