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

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

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

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

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

Multiply (1 + 3z) * (3 + 4z)
(1(3 + 4z) + 3z * (3 + 4z)) = 0
((3 * 1 + 4z * 1) + 3z * (3 + 4z)) = 0
((3 + 4z) + 3z * (3 + 4z)) = 0
(3 + 4z + (3 * 3z + 4z * 3z)) = 0
(3 + 4z + (9z + 12z2)) = 0

Combine like terms: 4z + 9z = 13z
(3 + 13z + 12z2) = 0

Solving
3 + 13z + 12z2 = 0

Solving for variable 'z'.

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

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

Simplifying
3 + 4z = 0

Solving
3 + 4z = 0

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

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

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

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

Divide each side by '4'.
z = -0.75

Simplifying
z = -0.75
Subproblem 2
Set the factor '(1 + 3z)' equal to zero and attempt to solve:

Simplifying
1 + 3z = 0

Solving
1 + 3z = 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 + 3z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3z = 0 + -1
3z = 0 + -1

Combine like terms: 0 + -1 = -1
3z = -1

Divide each side by '3'.
z = -0.3333333333

Simplifying
z = -0.3333333333
Solution
z = {-0.75, -0.3333333333}