3z^2+60z-21=0

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Solution for 3z^2+60z-21=0 equation: 


Simplifying
3z2 + 60z + -21 = 0

Reorder the terms:
-21 + 60z + 3z2 = 0

Solving
-21 + 60z + 3z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + 20z + z2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-7 + 20z + z2)' equal to zero and attempt to solve:

Simplifying
-7 + 20z + z2 = 0

Solving
-7 + 20z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 20z + 7 + z2 = 0 + 7

Reorder the terms:
-7 + 7 + 20z + z2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 20z + z2 = 0 + 7
20z + z2 = 0 + 7

Combine like terms: 0 + 7 = 7
20z + z2 = 7

The z term is 20z.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20z + 100 + z2 = 7 + 100

Reorder the terms:
100 + 20z + z2 = 7 + 100

Combine like terms: 7 + 100 = 107
100 + 20z + z2 = 107

Factor a perfect square on the left side:
(z + 10)(z + 10) = 107

Calculate the square root of the right side: 10.344080433

Break this problem into two subproblems by setting 
(z + 10) equal to 10.344080433 and -10.344080433.


Subproblem 1
z + 10 = 10.344080433

Simplifying
z + 10 = 10.344080433

Reorder the terms:
10 + z = 10.344080433

Solving
10 + z = 10.344080433

Solving for variable 'z'.

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 = 10.344080433 + -10

Combine like terms: 10 + -10 = 0
0 + z = 10.344080433 + -10
z = 10.344080433 + -10

Combine like terms: 10.344080433 + -10 = 0.344080433
z = 0.344080433

Simplifying
z = 0.344080433


Subproblem 2
z + 10 = -10.344080433

Simplifying
z + 10 = -10.344080433

Reorder the terms:
10 + z = -10.344080433

Solving
10 + z = -10.344080433

Solving for variable 'z'.

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 = -10.344080433 + -10

Combine like terms: 10 + -10 = 0
0 + z = -10.344080433 + -10
z = -10.344080433 + -10

Combine like terms: -10.344080433 + -10 = -20.344080433
z = -20.344080433

Simplifying
z = -20.344080433


Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.344080433, -20.344080433}
Solution
z = {0.344080433, -20.344080433}

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