10w^2+33w-7=0

Solution for 10w^2+33w-7=0 equation:

Simplifying
10w2 + 33w + -7 = 0

Reorder the terms:
-7 + 33w + 10w2 = 0

Solving
-7 + 33w + 10w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-7 + -2w)(1 + -5w) = 0

Subproblem 1
Set the factor '(-7 + -2w)' equal to zero and attempt to solve:

Simplifying
-7 + -2w = 0

Solving
-7 + -2w = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2w = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2w = 0 + 7
-2w = 0 + 7

Combine like terms: 0 + 7 = 7
-2w = 7

Divide each side by '-2'.
w = -3.5

Simplifying
w = -3.5
Subproblem 2
Set the factor '(1 + -5w)' equal to zero and attempt to solve:

Simplifying
1 + -5w = 0

Solving
1 + -5w = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5w = 0 + -1
-5w = 0 + -1

Combine like terms: 0 + -1 = -1
-5w = -1

Divide each side by '-5'.
w = 0.2

Simplifying
w = 0.2
Solution
w = {-3.5, 0.2}