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

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

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

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

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

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

Combine like terms: 1x + 6x = 7x
(6 + 7x + x2) = 2x

Solving
6 + 7x + x2 = 2x

Solving for variable 'x'.

Reorder the terms:
6 + 7x + -2x + x2 = 2x + -2x

Combine like terms: 7x + -2x = 5x
6 + 5x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
6 + 5x + x2 = 0

Factor a trinomial.
(3 + x)(2 + x) = 0

Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
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 = {-3, -2}