z(z+10)(z-10)=

Solution for z(z+10)(z-10)= equation:

Simplifying
z(z + 10)(z + -10) = 0

Reorder the terms:
z(10 + z)(z + -10) = 0

Reorder the terms:
z(10 + z)(-10 + z) = 0

Multiply (10 + z) * (-10 + z)
z(10(-10 + z) + z(-10 + z)) = 0
z((-10 * 10 + z * 10) + z(-10 + z)) = 0
z((-100 + 10z) + z(-10 + z)) = 0
z(-100 + 10z + (-10 * z + z * z)) = 0
z(-100 + 10z + (-10z + z2)) = 0

Combine like terms: 10z + -10z = 0
z(-100 + 0 + z2) = 0
z(-100 + z2) = 0
(-100 * z + z2 * z) = 0
(-100z + z3) = 0

Solving
-100z + z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-100 + z2) = 0

Factor a difference between two squares.
z((10 + z)(-10 + z)) = 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 '(10 + z)' equal to zero and attempt to solve:

Simplifying
10 + z = 0

Solving
10 + z = 0

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

Add '-10' to each side of the equation.
10 + -10 + z = 0 + -10

Combine like terms: 10 + -10 = 0
0 + z = 0 + -10
z = 0 + -10

Combine like terms: 0 + -10 = -10
z = -10

Simplifying
z = -10
Subproblem 3
Set the factor '(-10 + z)' equal to zero and attempt to solve:

Simplifying
-10 + z = 0

Solving
-10 + z = 0

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

Add '10' to each side of the equation.
-10 + 10 + z = 0 + 10

Combine like terms: -10 + 10 = 0
0 + z = 0 + 10
z = 0 + 10

Combine like terms: 0 + 10 = 10
z = 10

Simplifying
z = 10
Solution
z = {0, -10, 10}