3z(z-7)(z+1)=0

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Solution for 3z(z-7)(z+1)=0 equation: 


Simplifying
3z(z + -7)(z + 1) = 0

Reorder the terms:
3z(-7 + z)(z + 1) = 0

Reorder the terms:
3z(-7 + z)(1 + z) = 0

Multiply (-7 + z) * (1 + z)
3z(-7(1 + z) + z(1 + z)) = 0
3z((1 * -7 + z * -7) + z(1 + z)) = 0
3z((-7 + -7z) + z(1 + z)) = 0
3z(-7 + -7z + (1 * z + z * z)) = 0
3z(-7 + -7z + (1z + z2)) = 0

Combine like terms: -7z + 1z = -6z
3z(-7 + -6z + z2) = 0
(-7 * 3z + -6z * 3z + z2 * 3z) = 0
(-21z + -18z2 + 3z3) = 0

Solving
-21z + -18z2 + 3z3 = 0

Solving for variable 'z'.

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

Factor a trinomial.
3z((-1 + -1z)(7 + -1z)) = 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 + -1z)' equal to zero and attempt to solve:

Simplifying
-1 + -1z = 0

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

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

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

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

Simplifying
z = -1

Subproblem 3
Set the factor '(7 + -1z)' equal to zero and attempt to solve:

Simplifying
7 + -1z = 0

Solving
7 + -1z = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1z = 0 + -7
-1z = 0 + -7

Combine like terms: 0 + -7 = -7
-1z = -7

Divide each side by '-1'.
z = 7

Simplifying
z = 7
Solution
z = {0, -1, 7}

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