3w^2-45w+42=0

Solution for 3w^2-45w+42=0 equation:

Simplifying
3w2 + -45w + 42 = 0

Reorder the terms:
42 + -45w + 3w2 = 0

Solving
42 + -45w + 3w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3'.
3(14 + -15w + w2) = 0

Factor a trinomial.
3((1 + -1w)(14 + -1w)) = 0

Ignore the factor 3.
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 '(14 + -1w)' equal to zero and attempt to solve:

Simplifying
14 + -1w = 0

Solving
14 + -1w = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1w = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1w = 0 + -14
-1w = 0 + -14

Combine like terms: 0 + -14 = -14
-1w = -14

Divide each side by '-1'.
w = 14

Simplifying
w = 14
Solution
w = {1, 14}