(w+2)(w-1)+(10w+9)(w-1)=0

Solution for (w+2)(w-1)+(10w+9)(w-1)=0 equation:

Simplifying
(w + 2)(w + -1) + (10w + 9)(w + -1) = 0

Reorder the terms:
(2 + w)(w + -1) + (10w + 9)(w + -1) = 0

Reorder the terms:
(2 + w)(-1 + w) + (10w + 9)(w + -1) = 0

Multiply (2 + w) * (-1 + w)
(2(-1 + w) + w(-1 + w)) + (10w + 9)(w + -1) = 0
((-1 * 2 + w * 2) + w(-1 + w)) + (10w + 9)(w + -1) = 0
((-2 + 2w) + w(-1 + w)) + (10w + 9)(w + -1) = 0
(-2 + 2w + (-1 * w + w * w)) + (10w + 9)(w + -1) = 0
(-2 + 2w + (-1w + w2)) + (10w + 9)(w + -1) = 0

Combine like terms: 2w + -1w = 1w
(-2 + 1w + w2) + (10w + 9)(w + -1) = 0

Reorder the terms:
-2 + 1w + w2 + (9 + 10w)(w + -1) = 0

Reorder the terms:
-2 + 1w + w2 + (9 + 10w)(-1 + w) = 0

Multiply (9 + 10w) * (-1 + w)
-2 + 1w + w2 + (9(-1 + w) + 10w * (-1 + w)) = 0
-2 + 1w + w2 + ((-1 * 9 + w * 9) + 10w * (-1 + w)) = 0
-2 + 1w + w2 + ((-9 + 9w) + 10w * (-1 + w)) = 0
-2 + 1w + w2 + (-9 + 9w + (-1 * 10w + w * 10w)) = 0
-2 + 1w + w2 + (-9 + 9w + (-10w + 10w2)) = 0

Combine like terms: 9w + -10w = -1w
-2 + 1w + w2 + (-9 + -1w + 10w2) = 0

Reorder the terms:
-2 + -9 + 1w + -1w + w2 + 10w2 = 0

Combine like terms: -2 + -9 = -11
-11 + 1w + -1w + w2 + 10w2 = 0

Combine like terms: 1w + -1w = 0
-11 + 0 + w2 + 10w2 = 0
-11 + w2 + 10w2 = 0

Combine like terms: w2 + 10w2 = 11w2
-11 + 11w2 = 0

Solving
-11 + 11w2 = 0

Solving for variable 'w'.

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

Add '11' to each side of the equation.
-11 + 11 + 11w2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 11w2 = 0 + 11
11w2 = 0 + 11

Combine like terms: 0 + 11 = 11
11w2 = 11

Divide each side by '11'.
w2 = 1

Simplifying
w2 = 1

Take the square root of each side:
w = {-1, 1}