(w+6)(w+1)+(w-1)(w+2)=(w+4)(w+4)

Solution for (w+6)(w+1)+(w-1)(w+2)=(w+4)(w+4) equation:

Simplifying
(w + 6)(w + 1) + (w + -1)(w + 2) = (w + 4)(w + 4)

Reorder the terms:
(6 + w)(w + 1) + (w + -1)(w + 2) = (w + 4)(w + 4)

Reorder the terms:
(6 + w)(1 + w) + (w + -1)(w + 2) = (w + 4)(w + 4)

Multiply (6 + w) * (1 + w)
(6(1 + w) + w(1 + w)) + (w + -1)(w + 2) = (w + 4)(w + 4)
((1 * 6 + w * 6) + w(1 + w)) + (w + -1)(w + 2) = (w + 4)(w + 4)
((6 + 6w) + w(1 + w)) + (w + -1)(w + 2) = (w + 4)(w + 4)
(6 + 6w + (1 * w + w * w)) + (w + -1)(w + 2) = (w + 4)(w + 4)
(6 + 6w + (1w + w2)) + (w + -1)(w + 2) = (w + 4)(w + 4)

Combine like terms: 6w + 1w = 7w
(6 + 7w + w2) + (w + -1)(w + 2) = (w + 4)(w + 4)

Reorder the terms:
6 + 7w + w2 + (-1 + w)(w + 2) = (w + 4)(w + 4)

Reorder the terms:
6 + 7w + w2 + (-1 + w)(2 + w) = (w + 4)(w + 4)

Multiply (-1 + w) * (2 + w)
6 + 7w + w2 + (-1(2 + w) + w(2 + w)) = (w + 4)(w + 4)
6 + 7w + w2 + ((2 * -1 + w * -1) + w(2 + w)) = (w + 4)(w + 4)
6 + 7w + w2 + ((-2 + -1w) + w(2 + w)) = (w + 4)(w + 4)
6 + 7w + w2 + (-2 + -1w + (2 * w + w * w)) = (w + 4)(w + 4)
6 + 7w + w2 + (-2 + -1w + (2w + w2)) = (w + 4)(w + 4)

Combine like terms: -1w + 2w = 1w
6 + 7w + w2 + (-2 + 1w + w2) = (w + 4)(w + 4)

Reorder the terms:
6 + -2 + 7w + 1w + w2 + w2 = (w + 4)(w + 4)

Combine like terms: 6 + -2 = 4
4 + 7w + 1w + w2 + w2 = (w + 4)(w + 4)

Combine like terms: 7w + 1w = 8w
4 + 8w + w2 + w2 = (w + 4)(w + 4)

Combine like terms: w2 + w2 = 2w2
4 + 8w + 2w2 = (w + 4)(w + 4)

Reorder the terms:
4 + 8w + 2w2 = (4 + w)(w + 4)

Reorder the terms:
4 + 8w + 2w2 = (4 + w)(4 + w)

Multiply (4 + w) * (4 + w)
4 + 8w + 2w2 = (4(4 + w) + w(4 + w))
4 + 8w + 2w2 = ((4 * 4 + w * 4) + w(4 + w))
4 + 8w + 2w2 = ((16 + 4w) + w(4 + w))
4 + 8w + 2w2 = (16 + 4w + (4 * w + w * w))
4 + 8w + 2w2 = (16 + 4w + (4w + w2))

Combine like terms: 4w + 4w = 8w
4 + 8w + 2w2 = (16 + 8w + w2)

Add '-8w' to each side of the equation.
4 + 8w + -8w + 2w2 = 16 + 8w + -8w + w2

Combine like terms: 8w + -8w = 0
4 + 0 + 2w2 = 16 + 8w + -8w + w2
4 + 2w2 = 16 + 8w + -8w + w2

Combine like terms: 8w + -8w = 0
4 + 2w2 = 16 + 0 + w2
4 + 2w2 = 16 + w2

Solving
4 + 2w2 = 16 + w2

Solving for variable 'w'.

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

Add '-1w2' to each side of the equation.
4 + 2w2 + -1w2 = 16 + w2 + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
4 + 1w2 = 16 + w2 + -1w2

Combine like terms: w2 + -1w2 = 0
4 + 1w2 = 16 + 0
4 + 1w2 = 16

Add '-4' to each side of the equation.
4 + -4 + 1w2 = 16 + -4

Combine like terms: 4 + -4 = 0
0 + 1w2 = 16 + -4
1w2 = 16 + -4

Combine like terms: 16 + -4 = 12
1w2 = 12

Divide each side by '1'.
w2 = 12

Simplifying
w2 = 12

Take the square root of each side:
w = {-3.464101615, 3.464101615}