3z(z+4)=-1(z^2+9)

Solution for 3z(z+4)=-1(z^2+9) equation:

Simplifying
3z(z + 4) = -1(z2 + 9)

Reorder the terms:
3z(4 + z) = -1(z2 + 9)
(4 * 3z + z * 3z) = -1(z2 + 9)
(12z + 3z2) = -1(z2 + 9)

Reorder the terms:
12z + 3z2 = -1(9 + z2)
12z + 3z2 = (9 * -1 + z2 * -1)
12z + 3z2 = (-9 + -1z2)

Solving
12z + 3z2 = -9 + -1z2

Solving for variable 'z'.

Reorder the terms:
9 + 12z + 3z2 + z2 = -9 + -1z2 + 9 + z2

Combine like terms: 3z2 + z2 = 4z2
9 + 12z + 4z2 = -9 + -1z2 + 9 + z2

Reorder the terms:
9 + 12z + 4z2 = -9 + 9 + -1z2 + z2

Combine like terms: -9 + 9 = 0
9 + 12z + 4z2 = 0 + -1z2 + z2
9 + 12z + 4z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
9 + 12z + 4z2 = 0

Factor a trinomial.
(3 + 2z)(3 + 2z) = 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 '(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
Solution
z = {-1.5, -1.5}