(x+2)(x+3)=(x+1)(x+5)

Solution for (x+2)(x+3)=(x+1)(x+5) equation:

Simplifying
(x + 2)(x + 3) = (x + 1)(x + 5)

Reorder the terms:
(2 + x)(x + 3) = (x + 1)(x + 5)

Reorder the terms:
(2 + x)(3 + x) = (x + 1)(x + 5)

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x)) = (x + 1)(x + 5)
((3 * 2 + x * 2) + x(3 + x)) = (x + 1)(x + 5)
((6 + 2x) + x(3 + x)) = (x + 1)(x + 5)
(6 + 2x + (3 * x + x * x)) = (x + 1)(x + 5)
(6 + 2x + (3x + x2)) = (x + 1)(x + 5)

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2) = (x + 1)(x + 5)

Reorder the terms:
6 + 5x + x2 = (1 + x)(x + 5)

Reorder the terms:
6 + 5x + x2 = (1 + x)(5 + x)

Multiply (1 + x) * (5 + x)
6 + 5x + x2 = (1(5 + x) + x(5 + x))
6 + 5x + x2 = ((5 * 1 + x * 1) + x(5 + x))
6 + 5x + x2 = ((5 + 1x) + x(5 + x))
6 + 5x + x2 = (5 + 1x + (5 * x + x * x))
6 + 5x + x2 = (5 + 1x + (5x + x2))

Combine like terms: 1x + 5x = 6x
6 + 5x + x2 = (5 + 6x + x2)

Add '-1x2' to each side of the equation.
6 + 5x + x2 + -1x2 = 5 + 6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + 5x + 0 = 5 + 6x + x2 + -1x2
6 + 5x = 5 + 6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + 5x = 5 + 6x + 0
6 + 5x = 5 + 6x

Solving
6 + 5x = 5 + 6x

Solving for variable 'x'.

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

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

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

Combine like terms: 6x + -6x = 0
6 + -1x = 5 + 0
6 + -1x = 5

Add '-6' to each side of the equation.
6 + -6 + -1x = 5 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 5 + -6
-1x = 5 + -6

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

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

Simplifying
x = 1