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

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

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

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

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

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

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

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

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

Multiply (4 + x) * (4 + x)
6 + 7x + x2 = (4(4 + x) + x(4 + x))
6 + 7x + x2 = ((4 * 4 + x * 4) + x(4 + x))
6 + 7x + x2 = ((16 + 4x) + x(4 + x))
6 + 7x + x2 = (16 + 4x + (4 * x + x * x))
6 + 7x + x2 = (16 + 4x + (4x + x2))

Combine like terms: 4x + 4x = 8x
6 + 7x + x2 = (16 + 8x + x2)

Add '-1x2' to each side of the equation.
6 + 7x + x2 + -1x2 = 16 + 8x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + 7x + 0 = 16 + 8x + x2 + -1x2
6 + 7x = 16 + 8x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + 7x = 16 + 8x + 0
6 + 7x = 16 + 8x

Solving
6 + 7x = 16 + 8x

Solving for variable 'x'.

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

Add '-8x' to each side of the equation.
6 + 7x + -8x = 16 + 8x + -8x

Combine like terms: 7x + -8x = -1x
6 + -1x = 16 + 8x + -8x

Combine like terms: 8x + -8x = 0
6 + -1x = 16 + 0
6 + -1x = 16

Add '-6' to each side of the equation.
6 + -6 + -1x = 16 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 16 + -6
-1x = 16 + -6

Combine like terms: 16 + -6 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10