3z(z+5)(z+7)=0

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Solution for 3z(z+5)(z+7)=0 equation: 


Simplifying
3z(z + 5)(z + 7) = 0

Reorder the terms:
3z(5 + z)(z + 7) = 0

Reorder the terms:
3z(5 + z)(7 + z) = 0

Multiply (5 + z) * (7 + z)
3z(5(7 + z) + z(7 + z)) = 0
3z((7 * 5 + z * 5) + z(7 + z)) = 0
3z((35 + 5z) + z(7 + z)) = 0
3z(35 + 5z + (7 * z + z * z)) = 0
3z(35 + 5z + (7z + z2)) = 0

Combine like terms: 5z + 7z = 12z
3z(35 + 12z + z2) = 0
(35 * 3z + 12z * 3z + z2 * 3z) = 0
(105z + 36z2 + 3z3) = 0

Solving
105z + 36z2 + 3z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3z'.
3z(35 + 12z + z2) = 0

Factor a trinomial.
3z((7 + z)(5 + z)) = 0

Ignore the factor 3.

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 + z)' equal to zero and attempt to solve:

Simplifying
7 + z = 0

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

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

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

Simplifying
z = -7

Subproblem 3
Set the factor '(5 + z)' equal to zero and attempt to solve:

Simplifying
5 + z = 0

Solving
5 + z = 0

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

Add '-5' to each side of the equation.
5 + -5 + z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + z = 0 + -5
z = 0 + -5

Combine like terms: 0 + -5 = -5
z = -5

Simplifying
z = -5
Solution
z = {0, -7, -5}

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