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

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

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

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

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

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

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

Reorder the terms:
5 + 6x + x2 = (2 + x)(x + 3)

Reorder the terms:
5 + 6x + x2 = (2 + x)(3 + x)

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

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

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

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

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

Solving
5 + 6x = 6 + 5x

Solving for variable 'x'.

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

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

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

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

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

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

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

Divide each side by '1'.
x = 1

Simplifying
x = 1