(3w^2-5w+4)-(-w^2+2w+6)=

Solution for (3w^2-5w+4)-(-w^2+2w+6)= equation:

Simplifying
(3w2 + -5w + 4) + -1(-1w2 + 2w + 6) = 0

Reorder the terms:
(4 + -5w + 3w2) + -1(-1w2 + 2w + 6) = 0

Remove parenthesis around (4 + -5w + 3w2)
4 + -5w + 3w2 + -1(-1w2 + 2w + 6) = 0

Reorder the terms:
4 + -5w + 3w2 + -1(6 + 2w + -1w2) = 0
4 + -5w + 3w2 + (6 * -1 + 2w * -1 + -1w2 * -1) = 0
4 + -5w + 3w2 + (-6 + -2w + 1w2) = 0

Reorder the terms:
4 + -6 + -5w + -2w + 3w2 + 1w2 = 0

Combine like terms: 4 + -6 = -2
-2 + -5w + -2w + 3w2 + 1w2 = 0

Combine like terms: -5w + -2w = -7w
-2 + -7w + 3w2 + 1w2 = 0

Combine like terms: 3w2 + 1w2 = 4w2
-2 + -7w + 4w2 = 0

Solving
-2 + -7w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-1 + -4w)(2 + -1w) = 0

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

Simplifying
-1 + -4w = 0

Solving
-1 + -4w = 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 + -4w = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4w = 0 + 1
-4w = 0 + 1

Combine like terms: 0 + 1 = 1
-4w = 1

Divide each side by '-4'.
w = -0.25

Simplifying
w = -0.25
Subproblem 2
Set the factor '(2 + -1w)' equal to zero and attempt to solve:

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

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

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

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Solution
w = {-0.25, 2}