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

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

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

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

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

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

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

Solving
2 + 3x + x2 = 6x

Solving for variable 'x'.

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

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

Combine like terms: 6x + -6x = 0
2 + -3x + x2 = 0

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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

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