6w+3w(4w-2)=2(9w-3)

Solution for 6w+3w(4w-2)=2(9w-3) equation:

Simplifying
6w + 3w(4w + -2) = 2(9w + -3)

Reorder the terms:
6w + 3w(-2 + 4w) = 2(9w + -3)
6w + (-2 * 3w + 4w * 3w) = 2(9w + -3)
6w + (-6w + 12w2) = 2(9w + -3)

Combine like terms: 6w + -6w = 0
0 + 12w2 = 2(9w + -3)
12w2 = 2(9w + -3)

Reorder the terms:
12w2 = 2(-3 + 9w)
12w2 = (-3 * 2 + 9w * 2)
12w2 = (-6 + 18w)

Solving
12w2 = -6 + 18w

Solving for variable 'w'.

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

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

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

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

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

Factor a trinomial.
6((1 + -2w)(1 + -1w)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + -2w)' equal to zero and attempt to solve:

Simplifying
1 + -2w = 0

Solving
1 + -2w = 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 + -2w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2w = 0 + -1
-2w = 0 + -1

Combine like terms: 0 + -1 = -1
-2w = -1

Divide each side by '-2'.
w = 0.5

Simplifying
w = 0.5
Subproblem 2
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
Solution
w = {0.5, 1}