5670=3w^2-9w

Solution for 5670=3w^2-9w equation:

Simplifying
5670 = 3w2 + -9w

Reorder the terms:
5670 = -9w + 3w2

Solving
5670 = -9w + 3w2

Solving for variable 'w'.

Reorder the terms:
5670 + 9w + -3w2 = -9w + 9w + 3w2 + -3w2

Combine like terms: -9w + 9w = 0
5670 + 9w + -3w2 = 0 + 3w2 + -3w2
5670 + 9w + -3w2 = 3w2 + -3w2

Combine like terms: 3w2 + -3w2 = 0
5670 + 9w + -3w2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1890 + 3w + -1w2) = 0

Factor a trinomial.
3((45 + -1w)(42 + w)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(45 + -1w)' equal to zero and attempt to solve:

Simplifying
45 + -1w = 0

Solving
45 + -1w = 0

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

Add '-45' to each side of the equation.
45 + -45 + -1w = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -1w = 0 + -45
-1w = 0 + -45

Combine like terms: 0 + -45 = -45
-1w = -45

Divide each side by '-1'.
w = 45

Simplifying
w = 45
Subproblem 2
Set the factor '(42 + w)' equal to zero and attempt to solve:

Simplifying
42 + w = 0

Solving
42 + w = 0

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

Add '-42' to each side of the equation.
42 + -42 + w = 0 + -42

Combine like terms: 42 + -42 = 0
0 + w = 0 + -42
w = 0 + -42

Combine like terms: 0 + -42 = -42
w = -42

Simplifying
w = -42
Solution
w = {45, -42}