w(w+4)+15=(w-3)(w+9)

Solution for w(w+4)+15=(w-3)(w+9) equation:

Simplifying
w(w + 4) + 15 = (w + -3)(w + 9)

Reorder the terms:
w(4 + w) + 15 = (w + -3)(w + 9)
(4 * w + w * w) + 15 = (w + -3)(w + 9)
(4w + w2) + 15 = (w + -3)(w + 9)

Reorder the terms:
15 + 4w + w2 = (w + -3)(w + 9)

Reorder the terms:
15 + 4w + w2 = (-3 + w)(w + 9)

Reorder the terms:
15 + 4w + w2 = (-3 + w)(9 + w)

Multiply (-3 + w) * (9 + w)
15 + 4w + w2 = (-3(9 + w) + w(9 + w))
15 + 4w + w2 = ((9 * -3 + w * -3) + w(9 + w))
15 + 4w + w2 = ((-27 + -3w) + w(9 + w))
15 + 4w + w2 = (-27 + -3w + (9 * w + w * w))
15 + 4w + w2 = (-27 + -3w + (9w + w2))

Combine like terms: -3w + 9w = 6w
15 + 4w + w2 = (-27 + 6w + w2)

Add '-1w2' to each side of the equation.
15 + 4w + w2 + -1w2 = -27 + 6w + w2 + -1w2

Combine like terms: w2 + -1w2 = 0
15 + 4w + 0 = -27 + 6w + w2 + -1w2
15 + 4w = -27 + 6w + w2 + -1w2

Combine like terms: w2 + -1w2 = 0
15 + 4w = -27 + 6w + 0
15 + 4w = -27 + 6w

Solving
15 + 4w = -27 + 6w

Solving for variable 'w'.

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

Add '-6w' to each side of the equation.
15 + 4w + -6w = -27 + 6w + -6w

Combine like terms: 4w + -6w = -2w
15 + -2w = -27 + 6w + -6w

Combine like terms: 6w + -6w = 0
15 + -2w = -27 + 0
15 + -2w = -27

Add '-15' to each side of the equation.
15 + -15 + -2w = -27 + -15

Combine like terms: 15 + -15 = 0
0 + -2w = -27 + -15
-2w = -27 + -15

Combine like terms: -27 + -15 = -42
-2w = -42

Divide each side by '-2'.
w = 21

Simplifying
w = 21