=6w^2-12w-18

Solution for =6w^2-12w-18 equation:

Simplifying
0 = 6w2 + -12w + -18

Reorder the terms:
0 = -18 + -12w + 6w2

Solving
0 = -18 + -12w + 6w2

Solving for variable 'w'.

Combine like terms: 0 + 18 = 18
18 + 12w + -6w2 = -18 + -12w + 6w2 + 18 + 12w + -6w2

Reorder the terms:
18 + 12w + -6w2 = -18 + 18 + -12w + 12w + 6w2 + -6w2

Combine like terms: -18 + 18 = 0
18 + 12w + -6w2 = 0 + -12w + 12w + 6w2 + -6w2
18 + 12w + -6w2 = -12w + 12w + 6w2 + -6w2

Combine like terms: -12w + 12w = 0
18 + 12w + -6w2 = 0 + 6w2 + -6w2
18 + 12w + -6w2 = 6w2 + -6w2

Combine like terms: 6w2 + -6w2 = 0
18 + 12w + -6w2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + 2w + -1w2) = 0

Factor a trinomial.
6((3 + -1w)(1 + w)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 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 + -1w = 0 + -3

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

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

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Subproblem 2
Set the factor '(1 + w)' equal to zero and attempt to solve:

Simplifying
1 + w = 0

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

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

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

Simplifying
w = -1
Solution
w = {3, -1}