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

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

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

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

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

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

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

Reorder the terms for easier multiplication:
6 + 5x + x2 = 2x + 5x + 6

Reorder the terms:
6 + 5x + x2 = 6 + 2x + 5x

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

Add '-6' to each side of the equation.
6 + 5x + -6 + x2 = 6 + -6 + 7x

Reorder the terms:
6 + -6 + 5x + x2 = 6 + -6 + 7x

Combine like terms: 6 + -6 = 0
0 + 5x + x2 = 6 + -6 + 7x
5x + x2 = 6 + -6 + 7x

Combine like terms: 6 + -6 = 0
5x + x2 = 0 + 7x
5x + x2 = 7x

Solving
5x + x2 = 7x

Solving for variable 'x'.

Reorder the terms:
5x + -7x + x2 = 7x + -7x

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

Combine like terms: 7x + -7x = 0
-2x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-2 + 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 '(-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 = {0, 2}