0=w^2-3w-1890

Solution for 0=w^2-3w-1890 equation:

Simplifying
0 = w2 + -3w + -1890

Reorder the terms:
0 = -1890 + -3w + w2

Solving
0 = -1890 + -3w + w2

Solving for variable 'w'.

Combine like terms: 0 + 1890 = 1890
1890 + 3w + -1w2 = -1890 + -3w + w2 + 1890 + 3w + -1w2

Reorder the terms:
1890 + 3w + -1w2 = -1890 + 1890 + -3w + 3w + w2 + -1w2

Combine like terms: -1890 + 1890 = 0
1890 + 3w + -1w2 = 0 + -3w + 3w + w2 + -1w2
1890 + 3w + -1w2 = -3w + 3w + w2 + -1w2

Combine like terms: -3w + 3w = 0
1890 + 3w + -1w2 = 0 + w2 + -1w2
1890 + 3w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
1890 + 3w + -1w2 = 0

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

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}