4w^2-4w+6=3w+3

Solution for 4w^2-4w+6=3w+3 equation:

Simplifying
4w2 + -4w + 6 = 3w + 3

Reorder the terms:
6 + -4w + 4w2 = 3w + 3

Reorder the terms:
6 + -4w + 4w2 = 3 + 3w

Solving
6 + -4w + 4w2 = 3 + 3w

Solving for variable 'w'.

Reorder the terms:
6 + -3 + -4w + -3w + 4w2 = 3 + 3w + -3 + -3w

Combine like terms: 6 + -3 = 3
3 + -4w + -3w + 4w2 = 3 + 3w + -3 + -3w

Combine like terms: -4w + -3w = -7w
3 + -7w + 4w2 = 3 + 3w + -3 + -3w

Reorder the terms:
3 + -7w + 4w2 = 3 + -3 + 3w + -3w

Combine like terms: 3 + -3 = 0
3 + -7w + 4w2 = 0 + 3w + -3w
3 + -7w + 4w2 = 3w + -3w

Combine like terms: 3w + -3w = 0
3 + -7w + 4w2 = 0

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

Subproblem 1
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
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 = {0.75, 1}