50w^2+140w+90=0

Solution for 50w^2+140w+90=0 equation:

Simplifying
50w2 + 140w + 90 = 0

Reorder the terms:
90 + 140w + 50w2 = 0

Solving
90 + 140w + 50w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '10'.
10(9 + 14w + 5w2) = 0

Factor a trinomial.
10((9 + 5w)(1 + w)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(9 + 5w)' equal to zero and attempt to solve:

Simplifying
9 + 5w = 0

Solving
9 + 5w = 0

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

Add '-9' to each side of the equation.
9 + -9 + 5w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 5w = 0 + -9
5w = 0 + -9

Combine like terms: 0 + -9 = -9
5w = -9

Divide each side by '5'.
w = -1.8

Simplifying
w = -1.8
Subproblem 2
Set the factor '(1 + w)' equal to zero and attempt to solve:

Simplifying
1 + w = 0

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

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

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

Simplifying
w = -1
Solution
w = {-1.8, -1}