z(6z-7)(z+4)=0

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Solution for z(6z-7)(z+4)=0 equation: 


Simplifying
z(6z + -7)(z + 4) = 0

Reorder the terms:
z(-7 + 6z)(z + 4) = 0

Reorder the terms:
z(-7 + 6z)(4 + z) = 0

Multiply (-7 + 6z) * (4 + z)
z(-7(4 + z) + 6z * (4 + z)) = 0
z((4 * -7 + z * -7) + 6z * (4 + z)) = 0
z((-28 + -7z) + 6z * (4 + z)) = 0
z(-28 + -7z + (4 * 6z + z * 6z)) = 0
z(-28 + -7z + (24z + 6z2)) = 0

Combine like terms: -7z + 24z = 17z
z(-28 + 17z + 6z2) = 0
(-28 * z + 17z * z + 6z2 * z) = 0
(-28z + 17z2 + 6z3) = 0

Solving
-28z + 17z2 + 6z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-28 + 17z + 6z2) = 0

Factor a trinomial.
z((-4 + -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 '(-4 + -1z)' equal to zero and attempt to solve:

Simplifying
-4 + -1z = 0

Solving
-4 + -1z = 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 + -1z = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1z = 0 + 4
-1z = 0 + 4

Combine like terms: 0 + 4 = 4
-1z = 4

Divide each side by '-1'.
z = -4

Simplifying
z = -4

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, -4, 1.166666667}

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