6z^2+9z=7z-6

Solution for 6z^2+9z=7z-6 equation:

Simplifying
6z2 + 9z = 7z + -6

Reorder the terms:
9z + 6z2 = 7z + -6

Reorder the terms:
9z + 6z2 = -6 + 7z

Solving
9z + 6z2 = -6 + 7z

Solving for variable 'z'.

Reorder the terms:
6 + 9z + -7z + 6z2 = -6 + 7z + 6 + -7z

Combine like terms: 9z + -7z = 2z
6 + 2z + 6z2 = -6 + 7z + 6 + -7z

Reorder the terms:
6 + 2z + 6z2 = -6 + 6 + 7z + -7z

Combine like terms: -6 + 6 = 0
6 + 2z + 6z2 = 0 + 7z + -7z
6 + 2z + 6z2 = 7z + -7z

Combine like terms: 7z + -7z = 0
6 + 2z + 6z2 = 0

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

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

Simplifying
3 + z + 3z2 = 0

Solving
3 + z + 3z2 = 0

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

Divide each side by '3'.
1 + 0.3333333333z + z2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 0.3333333333z + -1 + z2 = 0 + -1

Reorder the terms:
1 + -1 + 0.3333333333z + z2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 0.3333333333z + z2 = 0 + -1
0.3333333333z + z2 = 0 + -1

Combine like terms: 0 + -1 = -1
0.3333333333z + z2 = -1

The z term is z.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.3333333333z + 0.25 + z2 = -1 + 0.25

Reorder the terms:
0.25 + 0.3333333333z + z2 = -1 + 0.25

Combine like terms: -1 + 0.25 = -0.75
0.25 + 0.3333333333z + z2 = -0.75

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = -0.75

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.