9z^2+6z+15=0

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Solution for 9z^2+6z+15=0 equation: 


Simplifying
9z2 + 6z + 15 = 0

Reorder the terms:
15 + 6z + 9z2 = 0

Solving
15 + 6z + 9z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + 2z + 3z2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(5 + 2z + 3z2)' equal to zero and attempt to solve:

Simplifying
5 + 2z + 3z2 = 0

Solving
5 + 2z + 3z2 = 0

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

Divide each side by '3'.
1.666666667 + 0.6666666667z + z2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + 0.6666666667z + -1.666666667 + z2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + 0.6666666667z + z2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + 0.6666666667z + z2 = 0 + -1.666666667
0.6666666667z + z2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
0.6666666667z + z2 = -1.666666667

The z term is 0.6666666667z.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667z + 0.1111111112 + z2 = -1.666666667 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667z + z2 = -1.666666667 + 0.1111111112

Combine like terms: -1.666666667 + 0.1111111112 = -1.5555555558
0.1111111112 + 0.6666666667z + z2 = -1.5555555558

Factor a perfect square on the left side:
(z + 0.3333333334)(z + 0.3333333334) = -1.5555555558

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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