2w(3w-1)=-9w+3

Solution for 2w(3w-1)=-9w+3 equation:

Simplifying
2w(3w + -1) = -9w + 3

Reorder the terms:
2w(-1 + 3w) = -9w + 3
(-1 * 2w + 3w * 2w) = -9w + 3
(-2w + 6w2) = -9w + 3

Reorder the terms:
-2w + 6w2 = 3 + -9w

Solving
-2w + 6w2 = 3 + -9w

Solving for variable 'w'.

Reorder the terms:
-3 + -2w + 9w + 6w2 = 3 + -9w + -3 + 9w

Combine like terms: -2w + 9w = 7w
-3 + 7w + 6w2 = 3 + -9w + -3 + 9w

Reorder the terms:
-3 + 7w + 6w2 = 3 + -3 + -9w + 9w

Combine like terms: 3 + -3 = 0
-3 + 7w + 6w2 = 0 + -9w + 9w
-3 + 7w + 6w2 = -9w + 9w

Combine like terms: -9w + 9w = 0
-3 + 7w + 6w2 = 0

Factor a trinomial.
(-3 + -2w)(1 + -3w) = 0

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

Simplifying
-3 + -2w = 0

Solving
-3 + -2w = 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 + -2w = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2w = 0 + 3
-2w = 0 + 3

Combine like terms: 0 + 3 = 3
-2w = 3

Divide each side by '-2'.
w = -1.5

Simplifying
w = -1.5
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 = {-1.5, 0.3333333333}