4z^2-64z-60=0

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Solution for 4z^2-64z-60=0 equation: 


Simplifying
4z2 + -64z + -60 = 0

Reorder the terms:
-60 + -64z + 4z2 = 0

Solving
-60 + -64z + 4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + -16z + z2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-15 + -16z + z2)' equal to zero and attempt to solve:

Simplifying
-15 + -16z + z2 = 0

Solving
-15 + -16z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -16z + 15 + z2 = 0 + 15

Reorder the terms:
-15 + 15 + -16z + z2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -16z + z2 = 0 + 15
-16z + z2 = 0 + 15

Combine like terms: 0 + 15 = 15
-16z + z2 = 15

The z term is -16z.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16z + 64 + z2 = 15 + 64

Reorder the terms:
64 + -16z + z2 = 15 + 64

Combine like terms: 15 + 64 = 79
64 + -16z + z2 = 79

Factor a perfect square on the left side:
(z + -8)(z + -8) = 79

Calculate the square root of the right side: 8.888194417

Break this problem into two subproblems by setting 
(z + -8) equal to 8.888194417 and -8.888194417.


Subproblem 1
z + -8 = 8.888194417

Simplifying
z + -8 = 8.888194417

Reorder the terms:
-8 + z = 8.888194417

Solving
-8 + z = 8.888194417

Solving for variable 'z'.

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

Add '8' to each side of the equation.
-8 + 8 + z = 8.888194417 + 8

Combine like terms: -8 + 8 = 0
0 + z = 8.888194417 + 8
z = 8.888194417 + 8

Combine like terms: 8.888194417 + 8 = 16.888194417
z = 16.888194417

Simplifying
z = 16.888194417


Subproblem 2
z + -8 = -8.888194417

Simplifying
z + -8 = -8.888194417

Reorder the terms:
-8 + z = -8.888194417

Solving
-8 + z = -8.888194417

Solving for variable 'z'.

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

Add '8' to each side of the equation.
-8 + 8 + z = -8.888194417 + 8

Combine like terms: -8 + 8 = 0
0 + z = -8.888194417 + 8
z = -8.888194417 + 8

Combine like terms: -8.888194417 + 8 = -0.888194417
z = -0.888194417

Simplifying
z = -0.888194417


Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {16.888194417, -0.888194417}
Solution
z = {16.888194417, -0.888194417}

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