4w^2+70w=74

Solution for 4w^2+70w=74 equation:

Simplifying
4w2 + 70w = 74

Reorder the terms:
70w + 4w2 = 74

Solving
70w + 4w2 = 74

Solving for variable 'w'.

Reorder the terms:
-74 + 70w + 4w2 = 74 + -74

Combine like terms: 74 + -74 = 0
-74 + 70w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-37 + 35w + 2w2) = 0

Factor a trinomial.
2((-37 + -2w)(1 + -1w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-37 + -2w)' equal to zero and attempt to solve:

Simplifying
-37 + -2w = 0

Solving
-37 + -2w = 0

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

Add '37' to each side of the equation.
-37 + 37 + -2w = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -2w = 0 + 37
-2w = 0 + 37

Combine like terms: 0 + 37 = 37
-2w = 37

Divide each side by '-2'.
w = -18.5

Simplifying
w = -18.5
Subproblem 2
Set the factor '(1 + -1w)' equal to zero and attempt to solve:

Simplifying
1 + -1w = 0

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

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

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

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

Simplifying
w = 1
Solution
w = {-18.5, 1}