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

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

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

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

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

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

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

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

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

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

Combine like terms: 5x + 1x = 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