(x+1)(x+6)=(x+5)(x+4)

Solution for (x+1)(x+6)=(x+5)(x+4) equation:

Simplifying
(x + 1)(x + 6) = (x + 5)(x + 4)

Reorder the terms:
(1 + x)(x + 6) = (x + 5)(x + 4)

Reorder the terms:
(1 + x)(6 + x) = (x + 5)(x + 4)

Multiply (1 + x) * (6 + x)
(1(6 + x) + x(6 + x)) = (x + 5)(x + 4)
((6 * 1 + x * 1) + x(6 + x)) = (x + 5)(x + 4)
((6 + 1x) + x(6 + x)) = (x + 5)(x + 4)
(6 + 1x + (6 * x + x * x)) = (x + 5)(x + 4)
(6 + 1x + (6x + x2)) = (x + 5)(x + 4)

Combine like terms: 1x + 6x = 7x
(6 + 7x + x2) = (x + 5)(x + 4)

Reorder the terms:
6 + 7x + x2 = (5 + x)(x + 4)

Reorder the terms:
6 + 7x + x2 = (5 + x)(4 + x)

Multiply (5 + x) * (4 + x)
6 + 7x + x2 = (5(4 + x) + x(4 + x))
6 + 7x + x2 = ((4 * 5 + x * 5) + x(4 + x))
6 + 7x + x2 = ((20 + 5x) + x(4 + x))
6 + 7x + x2 = (20 + 5x + (4 * x + x * x))
6 + 7x + x2 = (20 + 5x + (4x + x2))

Combine like terms: 5x + 4x = 9x
6 + 7x + x2 = (20 + 9x + x2)

Add '-1x2' to each side of the equation.
6 + 7x + x2 + -1x2 = 20 + 9x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + 7x + 0 = 20 + 9x + x2 + -1x2
6 + 7x = 20 + 9x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + 7x = 20 + 9x + 0
6 + 7x = 20 + 9x

Solving
6 + 7x = 20 + 9x

Solving for variable 'x'.

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

Add '-9x' to each side of the equation.
6 + 7x + -9x = 20 + 9x + -9x

Combine like terms: 7x + -9x = -2x
6 + -2x = 20 + 9x + -9x

Combine like terms: 9x + -9x = 0
6 + -2x = 20 + 0
6 + -2x = 20

Add '-6' to each side of the equation.
6 + -6 + -2x = 20 + -6

Combine like terms: 6 + -6 = 0
0 + -2x = 20 + -6
-2x = 20 + -6

Combine like terms: 20 + -6 = 14
-2x = 14

Divide each side by '-2'.
x = -7

Simplifying
x = -7