(w+2)(2w-1)=(w-2)(w+5)+15

Solution for (w+2)(2w-1)=(w-2)(w+5)+15 equation:

Simplifying
(w + 2)(2w + -1) = (w + -2)(w + 5) + 15

Reorder the terms:
(2 + w)(2w + -1) = (w + -2)(w + 5) + 15

Reorder the terms:
(2 + w)(-1 + 2w) = (w + -2)(w + 5) + 15

Multiply (2 + w) * (-1 + 2w)
(2(-1 + 2w) + w(-1 + 2w)) = (w + -2)(w + 5) + 15
((-1 * 2 + 2w * 2) + w(-1 + 2w)) = (w + -2)(w + 5) + 15
((-2 + 4w) + w(-1 + 2w)) = (w + -2)(w + 5) + 15
(-2 + 4w + (-1 * w + 2w * w)) = (w + -2)(w + 5) + 15
(-2 + 4w + (-1w + 2w2)) = (w + -2)(w + 5) + 15

Combine like terms: 4w + -1w = 3w
(-2 + 3w + 2w2) = (w + -2)(w + 5) + 15

Reorder the terms:
-2 + 3w + 2w2 = (-2 + w)(w + 5) + 15

Reorder the terms:
-2 + 3w + 2w2 = (-2 + w)(5 + w) + 15

Multiply (-2 + w) * (5 + w)
-2 + 3w + 2w2 = (-2(5 + w) + w(5 + w)) + 15
-2 + 3w + 2w2 = ((5 * -2 + w * -2) + w(5 + w)) + 15
-2 + 3w + 2w2 = ((-10 + -2w) + w(5 + w)) + 15
-2 + 3w + 2w2 = (-10 + -2w + (5 * w + w * w)) + 15
-2 + 3w + 2w2 = (-10 + -2w + (5w + w2)) + 15

Combine like terms: -2w + 5w = 3w
-2 + 3w + 2w2 = (-10 + 3w + w2) + 15

Reorder the terms:
-2 + 3w + 2w2 = -10 + 15 + 3w + w2

Combine like terms: -10 + 15 = 5
-2 + 3w + 2w2 = 5 + 3w + w2

Add '-3w' to each side of the equation.
-2 + 3w + -3w + 2w2 = 5 + 3w + -3w + w2

Combine like terms: 3w + -3w = 0
-2 + 0 + 2w2 = 5 + 3w + -3w + w2
-2 + 2w2 = 5 + 3w + -3w + w2

Combine like terms: 3w + -3w = 0
-2 + 2w2 = 5 + 0 + w2
-2 + 2w2 = 5 + w2

Solving
-2 + 2w2 = 5 + 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.
-2 + 2w2 + -1w2 = 5 + w2 + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
-2 + 1w2 = 5 + w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-2 + 1w2 = 5 + 0
-2 + 1w2 = 5

Add '2' to each side of the equation.
-2 + 2 + 1w2 = 5 + 2

Combine like terms: -2 + 2 = 0
0 + 1w2 = 5 + 2
1w2 = 5 + 2

Combine like terms: 5 + 2 = 7
1w2 = 7

Divide each side by '1'.
w2 = 7

Simplifying
w2 = 7

Take the square root of each side:
w = {-2.645751311, 2.645751311}