4w^2+3=13w

Solution for 4w^2+3=13w equation:

Simplifying
4w2 + 3 = 13w

Reorder the terms:
3 + 4w2 = 13w

Solving
3 + 4w2 = 13w

Solving for variable 'w'.

Reorder the terms:
3 + -13w + 4w2 = 13w + -13w

Combine like terms: 13w + -13w = 0
3 + -13w + 4w2 = 0

Factor a trinomial.
(1 + -4w)(3 + -1w) = 0

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

Simplifying
1 + -4w = 0

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

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

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

Divide each side by '-4'.
w = 0.25

Simplifying
w = 0.25
Subproblem 2
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 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 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Solution
w = {0.25, 3}