0=10w^2-22w-24

Solution for 0=10w^2-22w-24 equation:

Simplifying
0 = 10w2 + -22w + -24

Reorder the terms:
0 = -24 + -22w + 10w2

Solving
0 = -24 + -22w + 10w2

Solving for variable 'w'.

Combine like terms: 0 + 24 = 24
24 + 22w + -10w2 = -24 + -22w + 10w2 + 24 + 22w + -10w2

Reorder the terms:
24 + 22w + -10w2 = -24 + 24 + -22w + 22w + 10w2 + -10w2

Combine like terms: -24 + 24 = 0
24 + 22w + -10w2 = 0 + -22w + 22w + 10w2 + -10w2
24 + 22w + -10w2 = -22w + 22w + 10w2 + -10w2

Combine like terms: -22w + 22w = 0
24 + 22w + -10w2 = 0 + 10w2 + -10w2
24 + 22w + -10w2 = 10w2 + -10w2

Combine like terms: 10w2 + -10w2 = 0
24 + 22w + -10w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + 11w + -5w2) = 0

Factor a trinomial.
2((3 + -1w)(4 + 5w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Subproblem 2
Set the factor '(4 + 5w)' equal to zero and attempt to solve:

Simplifying
4 + 5w = 0

Solving
4 + 5w = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5w = 0 + -4
5w = 0 + -4

Combine like terms: 0 + -4 = -4
5w = -4

Divide each side by '5'.
w = -0.8

Simplifying
w = -0.8
Solution
w = {3, -0.8}