2w^2=5w-3

Solution for 2w^2=5w-3 equation:

Simplifying
2w2 = 5w + -3

Reorder the terms:
2w2 = -3 + 5w

Solving
2w2 = -3 + 5w

Solving for variable 'w'.

Reorder the terms:
3 + -5w + 2w2 = -3 + 5w + 3 + -5w

Reorder the terms:
3 + -5w + 2w2 = -3 + 3 + 5w + -5w

Combine like terms: -3 + 3 = 0
3 + -5w + 2w2 = 0 + 5w + -5w
3 + -5w + 2w2 = 5w + -5w

Combine like terms: 5w + -5w = 0
3 + -5w + 2w2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
w = {1, 1.5}