3z(3z+1)(5z-4)=

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Solution for 3z(3z+1)(5z-4)= equation: 


Simplifying
3z(3z + 1)(5z + -4) = 0

Reorder the terms:
3z(1 + 3z)(5z + -4) = 0

Reorder the terms:
3z(1 + 3z)(-4 + 5z) = 0

Multiply (1 + 3z) * (-4 + 5z)
3z(1(-4 + 5z) + 3z * (-4 + 5z)) = 0
3z((-4 * 1 + 5z * 1) + 3z * (-4 + 5z)) = 0
3z((-4 + 5z) + 3z * (-4 + 5z)) = 0
3z(-4 + 5z + (-4 * 3z + 5z * 3z)) = 0
3z(-4 + 5z + (-12z + 15z2)) = 0

Combine like terms: 5z + -12z = -7z
3z(-4 + -7z + 15z2) = 0
(-4 * 3z + -7z * 3z + 15z2 * 3z) = 0
(-12z + -21z2 + 45z3) = 0

Solving
-12z + -21z2 + 45z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3z'.
3z(-4 + -7z + 15z2) = 0

Factor a trinomial.
3z((-1 + -3z)(4 + -5z)) = 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 + -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

Subproblem 3
Set the factor '(4 + -5z)' equal to zero and attempt to solve:

Simplifying
4 + -5z = 0

Solving
4 + -5z = 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 + -5z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5z = 0 + -4
-5z = 0 + -4

Combine like terms: 0 + -4 = -4
-5z = -4

Divide each side by '-5'.
z = 0.8

Simplifying
z = 0.8
Solution
z = {0, -0.3333333333, 0.8}

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