36z^2+9z+15=0

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Solution for 36z^2+9z+15=0 equation: 


Simplifying
36z2 + 9z + 15 = 0

Reorder the terms:
15 + 9z + 36z2 = 0

Solving
15 + 9z + 36z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + 3z + 12z2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(5 + 3z + 12z2)' equal to zero and attempt to solve:

Simplifying
5 + 3z + 12z2 = 0

Solving
5 + 3z + 12z2 = 0

Begin completing the square.  Divide all terms by
12 the coefficient of the squared term: 

Divide each side by '12'.
0.4166666667 + 0.25z + z2 = 0

Move the constant term to the right:

Add '-0.4166666667' to each side of the equation.
0.4166666667 + 0.25z + -0.4166666667 + z2 = 0 + -0.4166666667

Reorder the terms:
0.4166666667 + -0.4166666667 + 0.25z + z2 = 0 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + 0.25z + z2 = 0 + -0.4166666667
0.25z + z2 = 0 + -0.4166666667

Combine like terms: 0 + -0.4166666667 = -0.4166666667
0.25z + z2 = -0.4166666667

The z term is 0.25z.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25z + 0.015625 + z2 = -0.4166666667 + 0.015625

Reorder the terms:
0.015625 + 0.25z + z2 = -0.4166666667 + 0.015625

Combine like terms: -0.4166666667 + 0.015625 = -0.4010416667
0.015625 + 0.25z + z2 = -0.4010416667

Factor a perfect square on the left side:
(z + 0.125)(z + 0.125) = -0.4010416667

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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