z(3z-7)(z+2)=0

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Solution for z(3z-7)(z+2)=0 equation: 


Simplifying
z(3z + -7)(z + 2) = 0

Reorder the terms:
z(-7 + 3z)(z + 2) = 0

Reorder the terms:
z(-7 + 3z)(2 + z) = 0

Multiply (-7 + 3z) * (2 + z)
z(-7(2 + z) + 3z * (2 + z)) = 0
z((2 * -7 + z * -7) + 3z * (2 + z)) = 0
z((-14 + -7z) + 3z * (2 + z)) = 0
z(-14 + -7z + (2 * 3z + z * 3z)) = 0
z(-14 + -7z + (6z + 3z2)) = 0

Combine like terms: -7z + 6z = -1z
z(-14 + -1z + 3z2) = 0
(-14 * z + -1z * z + 3z2 * z) = 0
(-14z + -1z2 + 3z3) = 0

Solving
-14z + -1z2 + 3z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-14 + -1z + 3z2) = 0

Factor a trinomial.
z((-2 + -1z)(7 + -3z)) = 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 '(-2 + -1z)' equal to zero and attempt to solve:

Simplifying
-2 + -1z = 0

Solving
-2 + -1z = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1z = 0 + 2

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

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

Divide each side by '-1'.
z = -2

Simplifying
z = -2

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

Simplifying
7 + -3z = 0

Solving
7 + -3z = 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 + -3z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3z = 0 + -7
-3z = 0 + -7

Combine like terms: 0 + -7 = -7
-3z = -7

Divide each side by '-3'.
z = 2.333333333

Simplifying
z = 2.333333333
Solution
z = {0, -2, 2.333333333}

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