2w^2+5w=52

Solution for 2w^2+5w=52 equation:

Simplifying
2w2 + 5w = 52

Reorder the terms:
5w + 2w2 = 52

Solving
5w + 2w2 = 52

Solving for variable 'w'.

Reorder the terms:
-52 + 5w + 2w2 = 52 + -52

Combine like terms: 52 + -52 = 0
-52 + 5w + 2w2 = 0

Factor a trinomial.
(-13 + -2w)(4 + -1w) = 0

Subproblem 1
Set the factor '(-13 + -2w)' equal to zero and attempt to solve:

Simplifying
-13 + -2w = 0

Solving
-13 + -2w = 0

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

Add '13' to each side of the equation.
-13 + 13 + -2w = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -2w = 0 + 13
-2w = 0 + 13

Combine like terms: 0 + 13 = 13
-2w = 13

Divide each side by '-2'.
w = -6.5

Simplifying
w = -6.5
Subproblem 2
Set the factor '(4 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

Solving
4 + -1w = 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 + -1w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1w = 0 + -4
-1w = 0 + -4

Combine like terms: 0 + -4 = -4
-1w = -4

Divide each side by '-1'.
w = 4

Simplifying
w = 4
Solution
w = {-6.5, 4}