(9z+2)(8z+6)=0

Solution for (9z+2)(8z+6)=0 equation:

Simplifying
(9z + 2)(8z + 6) = 0

Reorder the terms:
(2 + 9z)(8z + 6) = 0

Reorder the terms:
(2 + 9z)(6 + 8z) = 0

Multiply (2 + 9z) * (6 + 8z)
(2(6 + 8z) + 9z * (6 + 8z)) = 0
((6 * 2 + 8z * 2) + 9z * (6 + 8z)) = 0
((12 + 16z) + 9z * (6 + 8z)) = 0
(12 + 16z + (6 * 9z + 8z * 9z)) = 0
(12 + 16z + (54z + 72z2)) = 0

Combine like terms: 16z + 54z = 70z
(12 + 70z + 72z2) = 0

Solving
12 + 70z + 72z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 35z + 36z2) = 0

Factor a trinomial.
2((3 + 4z)(2 + 9z)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 4z)' equal to zero and attempt to solve:

Simplifying
3 + 4z = 0

Solving
3 + 4z = 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 + 4z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4z = 0 + -3
4z = 0 + -3

Combine like terms: 0 + -3 = -3
4z = -3

Divide each side by '4'.
z = -0.75

Simplifying
z = -0.75
Subproblem 2
Set the factor '(2 + 9z)' equal to zero and attempt to solve:

Simplifying
2 + 9z = 0

Solving
2 + 9z = 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 + 9z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 9z = 0 + -2
9z = 0 + -2

Combine like terms: 0 + -2 = -2
9z = -2

Divide each side by '9'.
z = -0.2222222222

Simplifying
z = -0.2222222222
Solution
z = {-0.75, -0.2222222222}