3w^2-3=8w

Solution for 3w^2-3=8w equation:

Simplifying
3w2 + -3 = 8w

Reorder the terms:
-3 + 3w2 = 8w

Solving
-3 + 3w2 = 8w

Solving for variable 'w'.

Reorder the terms:
-3 + -8w + 3w2 = 8w + -8w

Combine like terms: 8w + -8w = 0
-3 + -8w + 3w2 = 0

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

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

Simplifying
-1 + -3w = 0

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

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

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

Divide each side by '-3'.
w = -0.3333333333

Simplifying
w = -0.3333333333
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 = {-0.3333333333, 3}