3w^2-9w=5670

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

Simplifying
3w2 + -9w = 5670

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

Solving
-9w + 3w2 = 5670

Solving for variable 'w'.

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

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

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

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-42 + -1w)' equal to zero and attempt to solve:

Simplifying
-42 + -1w = 0

Solving
-42 + -1w = 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 + -1w = 0 + 42

Combine like terms: -42 + 42 = 0
0 + -1w = 0 + 42
-1w = 0 + 42

Combine like terms: 0 + 42 = 42
-1w = 42

Divide each side by '-1'.
w = -42

Simplifying
w = -42
Subproblem 2
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
Solution
w = {-42, 45}