z(6z-7)(z+3)=0

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Solution for z(6z-7)(z+3)=0 equation: 


Simplifying
z(6z + -7)(z + 3) = 0

Reorder the terms:
z(-7 + 6z)(z + 3) = 0

Reorder the terms:
z(-7 + 6z)(3 + z) = 0

Multiply (-7 + 6z) * (3 + z)
z(-7(3 + z) + 6z * (3 + z)) = 0
z((3 * -7 + z * -7) + 6z * (3 + z)) = 0
z((-21 + -7z) + 6z * (3 + z)) = 0
z(-21 + -7z + (3 * 6z + z * 6z)) = 0
z(-21 + -7z + (18z + 6z2)) = 0

Combine like terms: -7z + 18z = 11z
z(-21 + 11z + 6z2) = 0
(-21 * z + 11z * z + 6z2 * z) = 0
(-21z + 11z2 + 6z3) = 0

Solving
-21z + 11z2 + 6z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-21 + 11z + 6z2) = 0

Factor a trinomial.
z((-3 + -1z)(7 + -6z)) = 0


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 '(-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 3
Set the factor '(7 + -6z)' equal to zero and attempt to solve:

Simplifying
7 + -6z = 0

Solving
7 + -6z = 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 + -6z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6z = 0 + -7
-6z = 0 + -7

Combine like terms: 0 + -7 = -7
-6z = -7

Divide each side by '-6'.
z = 1.166666667

Simplifying
z = 1.166666667
Solution
z = {0, -3, 1.166666667}

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