42w^2-5w-3=0

Solution for 42w^2-5w-3=0 equation:

Simplifying
42w2 + -5w + -3 = 0

Reorder the terms:
-3 + -5w + 42w2 = 0

Solving
-3 + -5w + 42w2 = 0

Solving for variable 'w'.

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

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

Simplifying
-3 + -14w = 0

Solving
-3 + -14w = 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 + -14w = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -14w = 0 + 3
-14w = 0 + 3

Combine like terms: 0 + 3 = 3
-14w = 3

Divide each side by '-14'.
w = -0.2142857143

Simplifying
w = -0.2142857143
Subproblem 2
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
Solution
w = {-0.2142857143, 0.3333333333}