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

Solution for (6+z)(4z-3)=0 equation:

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

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

Multiply (6 + z) * (-3 + 4z)
(6(-3 + 4z) + z(-3 + 4z)) = 0
((-3 * 6 + 4z * 6) + z(-3 + 4z)) = 0
((-18 + 24z) + z(-3 + 4z)) = 0
(-18 + 24z + (-3 * z + 4z * z)) = 0
(-18 + 24z + (-3z + 4z2)) = 0

Combine like terms: 24z + -3z = 21z
(-18 + 21z + 4z2) = 0

Solving
-18 + 21z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-6 + -1z)(3 + -4z) = 0

Subproblem 1
Set the factor '(-6 + -1z)' equal to zero and attempt to solve:

Simplifying
-6 + -1z = 0

Solving
-6 + -1z = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1z = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1z = 0 + 6
-1z = 0 + 6

Combine like terms: 0 + 6 = 6
-1z = 6

Divide each side by '-1'.
z = -6

Simplifying
z = -6
Subproblem 2
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
Solution
z = {-6, 0.75}