(-7w^2+5w-4)+(3w^2+2w+1)=

Solution for (-7w^2+5w-4)+(3w^2+2w+1)= equation:

Simplifying
(-7w2 + 5w + -4) + (3w2 + 2w + 1) = 0

Reorder the terms:
(-4 + 5w + -7w2) + (3w2 + 2w + 1) = 0

Remove parenthesis around (-4 + 5w + -7w2)
-4 + 5w + -7w2 + (3w2 + 2w + 1) = 0

Reorder the terms:
-4 + 5w + -7w2 + (1 + 2w + 3w2) = 0

Remove parenthesis around (1 + 2w + 3w2)
-4 + 5w + -7w2 + 1 + 2w + 3w2 = 0

Reorder the terms:
-4 + 1 + 5w + 2w + -7w2 + 3w2 = 0

Combine like terms: -4 + 1 = -3
-3 + 5w + 2w + -7w2 + 3w2 = 0

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

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

Solving
-3 + 7w + -4w2 = 0

Solving for variable 'w'.

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

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

Simplifying
-1 + w = 0

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

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

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

Simplifying
w = 1
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 = {1, 0.75}