9(z+1)(z+1)+12=16

Solution for 9(z+1)(z+1)+12=16 equation:

Simplifying
9(z + 1)(z + 1) + 12 = 16

Reorder the terms:
9(1 + z)(z + 1) + 12 = 16

Reorder the terms:
9(1 + z)(1 + z) + 12 = 16

Multiply (1 + z) * (1 + z)
9(1(1 + z) + z(1 + z)) + 12 = 16
9((1 * 1 + z * 1) + z(1 + z)) + 12 = 16
9((1 + 1z) + z(1 + z)) + 12 = 16
9(1 + 1z + (1 * z + z * z)) + 12 = 16
9(1 + 1z + (1z + z2)) + 12 = 16

Combine like terms: 1z + 1z = 2z
9(1 + 2z + z2) + 12 = 16
(1 * 9 + 2z * 9 + z2 * 9) + 12 = 16
(9 + 18z + 9z2) + 12 = 16

Reorder the terms:
9 + 12 + 18z + 9z2 = 16

Combine like terms: 9 + 12 = 21
21 + 18z + 9z2 = 16

Solving
21 + 18z + 9z2 = 16

Solving for variable 'z'.

Reorder the terms:
21 + -16 + 18z + 9z2 = 16 + -16

Combine like terms: 21 + -16 = 5
5 + 18z + 9z2 = 16 + -16

Combine like terms: 16 + -16 = 0
5 + 18z + 9z2 = 0

Factor a trinomial.
(5 + 3z)(1 + 3z) = 0

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

Simplifying
5 + 3z = 0

Solving
5 + 3z = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3z = 0 + -5
3z = 0 + -5

Combine like terms: 0 + -5 = -5
3z = -5

Divide each side by '3'.
z = -1.666666667

Simplifying
z = -1.666666667
Subproblem 2
Set the factor '(1 + 3z)' equal to zero and attempt to solve:

Simplifying
1 + 3z = 0

Solving
1 + 3z = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3z = 0 + -1
3z = 0 + -1

Combine like terms: 0 + -1 = -1
3z = -1

Divide each side by '3'.
z = -0.3333333333

Simplifying
z = -0.3333333333
Solution
z = {-1.666666667, -0.3333333333}