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

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

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

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

Multiply (1 + z) * (4 + 3z)
(1(4 + 3z) + z(4 + 3z)) = 0
((4 * 1 + 3z * 1) + z(4 + 3z)) = 0
((4 + 3z) + z(4 + 3z)) = 0
(4 + 3z + (4 * z + 3z * z)) = 0
(4 + 3z + (4z + 3z2)) = 0

Combine like terms: 3z + 4z = 7z
(4 + 7z + 3z2) = 0

Solving
4 + 7z + 3z2 = 0

Solving for variable 'z'.

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

Subproblem 1
Set the factor '(4 + 3z)' equal to zero and attempt to solve:

Simplifying
4 + 3z = 0

Solving
4 + 3z = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3z = 0 + -4
3z = 0 + -4

Combine like terms: 0 + -4 = -4
3z = -4

Divide each side by '3'.
z = -1.333333333

Simplifying
z = -1.333333333
Subproblem 2
Set the factor '(1 + z)' equal to zero and attempt to solve:

Simplifying
1 + z = 0

Solving
1 + z = 0

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

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

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

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

Simplifying
z = -1
Solution
z = {-1.333333333, -1}