(1+w)(4w+3)=0

Solution for (1+w)(4w+3)=0 equation:

Simplifying
(1 + w)(4w + 3) = 0

Reorder the terms:
(1 + w)(3 + 4w) = 0

Multiply (1 + w) * (3 + 4w)
(1(3 + 4w) + w(3 + 4w)) = 0
((3 * 1 + 4w * 1) + w(3 + 4w)) = 0
((3 + 4w) + w(3 + 4w)) = 0
(3 + 4w + (3 * w + 4w * w)) = 0
(3 + 4w + (3w + 4w2)) = 0

Combine like terms: 4w + 3w = 7w
(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}