3w(4w-3)=4w-3

Solution for 3w(4w-3)=4w-3 equation:

Simplifying
3w(4w + -3) = 4w + -3

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

Reorder the terms:
-9w + 12w2 = -3 + 4w

Solving
-9w + 12w2 = -3 + 4w

Solving for variable 'w'.

Reorder the terms:
3 + -9w + -4w + 12w2 = -3 + 4w + 3 + -4w

Combine like terms: -9w + -4w = -13w
3 + -13w + 12w2 = -3 + 4w + 3 + -4w

Reorder the terms:
3 + -13w + 12w2 = -3 + 3 + 4w + -4w

Combine like terms: -3 + 3 = 0
3 + -13w + 12w2 = 0 + 4w + -4w
3 + -13w + 12w2 = 4w + -4w

Combine like terms: 4w + -4w = 0
3 + -13w + 12w2 = 0

Factor a trinomial.
(1 + -3w)(3 + -4w) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -4w)' equal to zero and attempt to solve:

Simplifying
3 + -4w = 0

Solving
3 + -4w = 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 + -4w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4w = 0 + -3
-4w = 0 + -3

Combine like terms: 0 + -3 = -3
-4w = -3

Divide each side by '-4'.
w = 0.75

Simplifying
w = 0.75
Solution
w = {0.3333333333, 0.75}