(x+2)(x+3)=x+5x+6

Solution for (x+2)(x+3)=x+5x+6 equation:

Simplifying
(x + 2)(x + 3) = x + 5x + 6

Reorder the terms:
(2 + x)(x + 3) = x + 5x + 6

Reorder the terms:
(2 + x)(3 + x) = x + 5x + 6

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x)) = x + 5x + 6
((3 * 2 + x * 2) + x(3 + x)) = x + 5x + 6
((6 + 2x) + x(3 + x)) = x + 5x + 6
(6 + 2x + (3 * x + x * x)) = x + 5x + 6
(6 + 2x + (3x + x2)) = x + 5x + 6

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2) = x + 5x + 6

Reorder the terms:
6 + 5x + x2 = 6 + x + 5x

Combine like terms: x + 5x = 6x
6 + 5x + x2 = 6 + 6x

Add '-6' to each side of the equation.
6 + 5x + -6 + x2 = 6 + -6 + 6x

Reorder the terms:
6 + -6 + 5x + x2 = 6 + -6 + 6x

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

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

Solving
5x + x2 = 6x

Solving for variable 'x'.

Reorder the terms:
5x + -6x + x2 = 6x + -6x

Combine like terms: 5x + -6x = -1x
-1x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-1x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

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

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

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

Simplifying
x = 1
Solution
x = {0, 1}