(1+w)(4w+6)=0

Solution for (1+w)(4w+6)=0 equation:

Simplifying
(1 + w)(4w + 6) = 0

Reorder the terms:
(1 + w)(6 + 4w) = 0

Multiply (1 + w) * (6 + 4w)
(1(6 + 4w) + w(6 + 4w)) = 0
((6 * 1 + 4w * 1) + w(6 + 4w)) = 0
((6 + 4w) + w(6 + 4w)) = 0
(6 + 4w + (6 * w + 4w * w)) = 0
(6 + 4w + (6w + 4w2)) = 0

Combine like terms: 4w + 6w = 10w
(6 + 10w + 4w2) = 0

Solving
6 + 10w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 5w + 2w2) = 0

Factor a trinomial.
2((3 + 2w)(1 + w)) = 0

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

Simplifying
3 + 2w = 0

Solving
3 + 2w = 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 + 2w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2w = 0 + -3
2w = 0 + -3

Combine like terms: 0 + -3 = -3
2w = -3

Divide each side by '2'.
w = -1.5

Simplifying
w = -1.5
Subproblem 2
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
Solution
w = {-1.5, -1}