3z(2z+1)(3z-5)=

Solution for 3z(2z+1)(3z-5)= equation:

Simplifying
3z(2z + 1)(3z + -5) = 0

Reorder the terms:
3z(1 + 2z)(3z + -5) = 0

Reorder the terms:
3z(1 + 2z)(-5 + 3z) = 0

Multiply (1 + 2z) * (-5 + 3z)
3z(1(-5 + 3z) + 2z * (-5 + 3z)) = 0
3z((-5 * 1 + 3z * 1) + 2z * (-5 + 3z)) = 0
3z((-5 + 3z) + 2z * (-5 + 3z)) = 0
3z(-5 + 3z + (-5 * 2z + 3z * 2z)) = 0
3z(-5 + 3z + (-10z + 6z2)) = 0

Combine like terms: 3z + -10z = -7z
3z(-5 + -7z + 6z2) = 0
(-5 * 3z + -7z * 3z + 6z2 * 3z) = 0
(-15z + -21z2 + 18z3) = 0

Solving
-15z + -21z2 + 18z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3z'.
3z(-5 + -7z + 6z2) = 0

Factor a trinomial.
3z((-1 + -2z)(5 + -3z)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Subproblem 2
Set the factor '(-1 + -2z)' equal to zero and attempt to solve:

Simplifying
-1 + -2z = 0

Solving
-1 + -2z = 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 + -2z = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2z = 0 + 1
-2z = 0 + 1

Combine like terms: 0 + 1 = 1
-2z = 1

Divide each side by '-2'.
z = -0.5

Simplifying
z = -0.5
Subproblem 3
Set the factor '(5 + -3z)' equal to zero and attempt to solve:

Simplifying
5 + -3z = 0

Solving
5 + -3z = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3z = 0 + -5
-3z = 0 + -5

Combine like terms: 0 + -5 = -5
-3z = -5

Divide each side by '-3'.
z = 1.666666667

Simplifying
z = 1.666666667
Solution
z = {0, -0.5, 1.666666667}