4w^2-18w=10

Solution for 4w^2-18w=10 equation:

Simplifying
4w2 + -18w = 10

Reorder the terms:
-18w + 4w2 = 10

Solving
-18w + 4w2 = 10

Solving for variable 'w'.

Reorder the terms:
-10 + -18w + 4w2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -18w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -9w + 2w2) = 0

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

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

Simplifying
-1 + -2w = 0

Solving
-1 + -2w = 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 + -2w = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2w = 0 + 1
-2w = 0 + 1

Combine like terms: 0 + 1 = 1
-2w = 1

Divide each side by '-2'.
w = -0.5

Simplifying
w = -0.5
Subproblem 2
Set the factor '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 0

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

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

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

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

Divide each side by '-1'.
w = 5

Simplifying
w = 5
Solution
w = {-0.5, 5}