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

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

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

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

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

Combine like terms: 9z + -4z = 5z
(-12 + 5z + 3z2) = 0

Solving
-12 + 5z + 3z2 = 0

Solving for variable 'z'.

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

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

Simplifying
-3 + -1z = 0

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

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

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

Divide each side by '-1'.
z = -3

Simplifying
z = -3
Subproblem 2
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
Solution
z = {-3, 1.333333333}