2w^2=7w+15

Solution for 2w^2=7w+15 equation:

Simplifying
2w2 = 7w + 15

Reorder the terms:
2w2 = 15 + 7w

Solving
2w2 = 15 + 7w

Solving for variable 'w'.

Reorder the terms:
-15 + -7w + 2w2 = 15 + 7w + -15 + -7w

Reorder the terms:
-15 + -7w + 2w2 = 15 + -15 + 7w + -7w

Combine like terms: 15 + -15 = 0
-15 + -7w + 2w2 = 0 + 7w + -7w
-15 + -7w + 2w2 = 7w + -7w

Combine like terms: 7w + -7w = 0
-15 + -7w + 2w2 = 0

Factor a trinomial.
(-3 + -2w)(5 + -1w) = 0

Subproblem 1
Set the factor '(-3 + -2w)' equal to zero and attempt to solve:

Simplifying
-3 + -2w = 0

Solving
-3 + -2w = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2w = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2w = 0 + 3
-2w = 0 + 3

Combine like terms: 0 + 3 = 3
-2w = 3

Divide each side by '-2'.
w = -1.5

Simplifying
w = -1.5
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 = {-1.5, 5}