(7z+6)(9z-2)=0

Solution for (7z+6)(9z-2)=0 equation:

Simplifying
(7z + 6)(9z + -2) = 0

Reorder the terms:
(6 + 7z)(9z + -2) = 0

Reorder the terms:
(6 + 7z)(-2 + 9z) = 0

Multiply (6 + 7z) * (-2 + 9z)
(6(-2 + 9z) + 7z * (-2 + 9z)) = 0
((-2 * 6 + 9z * 6) + 7z * (-2 + 9z)) = 0
((-12 + 54z) + 7z * (-2 + 9z)) = 0
(-12 + 54z + (-2 * 7z + 9z * 7z)) = 0
(-12 + 54z + (-14z + 63z2)) = 0

Combine like terms: 54z + -14z = 40z
(-12 + 40z + 63z2) = 0

Solving
-12 + 40z + 63z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-6 + -7z)(2 + -9z) = 0

Subproblem 1
Set the factor '(-6 + -7z)' equal to zero and attempt to solve:

Simplifying
-6 + -7z = 0

Solving
-6 + -7z = 0

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

Add '6' to each side of the equation.
-6 + 6 + -7z = 0 + 6

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

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

Divide each side by '-7'.
z = -0.8571428571

Simplifying
z = -0.8571428571
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 = {-0.8571428571, 0.2222222222}