z(z+7)(z-15)=0

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Solution for z(z+7)(z-15)=0 equation: 


Simplifying
z(z + 7)(z + -15) = 0

Reorder the terms:
z(7 + z)(z + -15) = 0

Reorder the terms:
z(7 + z)(-15 + z) = 0

Multiply (7 + z) * (-15 + z)
z(7(-15 + z) + z(-15 + z)) = 0
z((-15 * 7 + z * 7) + z(-15 + z)) = 0
z((-105 + 7z) + z(-15 + z)) = 0
z(-105 + 7z + (-15 * z + z * z)) = 0
z(-105 + 7z + (-15z + z2)) = 0

Combine like terms: 7z + -15z = -8z
z(-105 + -8z + z2) = 0
(-105 * z + -8z * z + z2 * z) = 0
(-105z + -8z2 + z3) = 0

Solving
-105z + -8z2 + z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-105 + -8z + z2) = 0

Factor a trinomial.
z((-7 + -1z)(15 + -1z)) = 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 '(-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

Subproblem 3
Set the factor '(15 + -1z)' equal to zero and attempt to solve:

Simplifying
15 + -1z = 0

Solving
15 + -1z = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1z = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1z = 0 + -15
-1z = 0 + -15

Combine like terms: 0 + -15 = -15
-1z = -15

Divide each side by '-1'.
z = 15

Simplifying
z = 15
Solution
z = {0, -7, 15}

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