6(z^2+1)=-13z

Solution for 6(z^2+1)=-13z equation:

Simplifying
6(z2 + 1) = -13z

Reorder the terms:
6(1 + z2) = -13z
(1 * 6 + z2 * 6) = -13z
(6 + 6z2) = -13z

Solving
6 + 6z2 = -13z

Solving for variable 'z'.

Reorder the terms:
6 + 13z + 6z2 = -13z + 13z

Combine like terms: -13z + 13z = 0
6 + 13z + 6z2 = 0

Factor a trinomial.
(3 + 2z)(2 + 3z) = 0

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

Simplifying
3 + 2z = 0

Solving
3 + 2z = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2z = 0 + -3
2z = 0 + -3

Combine like terms: 0 + -3 = -3
2z = -3

Divide each side by '2'.
z = -1.5

Simplifying
z = -1.5
Subproblem 2
Set the factor '(2 + 3z)' equal to zero and attempt to solve:

Simplifying
2 + 3z = 0

Solving
2 + 3z = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3z = 0 + -2
3z = 0 + -2

Combine like terms: 0 + -2 = -2
3z = -2

Divide each side by '3'.
z = -0.6666666667

Simplifying
z = -0.6666666667
Solution
z = {-1.5, -0.6666666667}