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

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

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

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

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

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

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

Reorder the terms:
1 + 2x + x2 = (5 + x)(x + 6)

Reorder the terms:
1 + 2x + x2 = (5 + x)(6 + x)

Multiply (5 + x) * (6 + x)
1 + 2x + x2 = (5(6 + x) + x(6 + x))
1 + 2x + x2 = ((6 * 5 + x * 5) + x(6 + x))
1 + 2x + x2 = ((30 + 5x) + x(6 + x))
1 + 2x + x2 = (30 + 5x + (6 * x + x * x))
1 + 2x + x2 = (30 + 5x + (6x + x2))

Combine like terms: 5x + 6x = 11x
1 + 2x + x2 = (30 + 11x + x2)

Add '-1x2' to each side of the equation.
1 + 2x + x2 + -1x2 = 30 + 11x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1 + 2x + 0 = 30 + 11x + x2 + -1x2
1 + 2x = 30 + 11x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1 + 2x = 30 + 11x + 0
1 + 2x = 30 + 11x

Solving
1 + 2x = 30 + 11x

Solving for variable 'x'.

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

Add '-11x' to each side of the equation.
1 + 2x + -11x = 30 + 11x + -11x

Combine like terms: 2x + -11x = -9x
1 + -9x = 30 + 11x + -11x

Combine like terms: 11x + -11x = 0
1 + -9x = 30 + 0
1 + -9x = 30

Add '-1' to each side of the equation.
1 + -1 + -9x = 30 + -1

Combine like terms: 1 + -1 = 0
0 + -9x = 30 + -1
-9x = 30 + -1

Combine like terms: 30 + -1 = 29
-9x = 29

Divide each side by '-9'.
x = -3.222222222

Simplifying
x = -3.222222222