(7z+9)(4z-6)=0

Solution for (7z+9)(4z-6)=0 equation:

Simplifying
(7z + 9)(4z + -6) = 0

Reorder the terms:
(9 + 7z)(4z + -6) = 0

Reorder the terms:
(9 + 7z)(-6 + 4z) = 0

Multiply (9 + 7z) * (-6 + 4z)
(9(-6 + 4z) + 7z * (-6 + 4z)) = 0
((-6 * 9 + 4z * 9) + 7z * (-6 + 4z)) = 0
((-54 + 36z) + 7z * (-6 + 4z)) = 0
(-54 + 36z + (-6 * 7z + 4z * 7z)) = 0
(-54 + 36z + (-42z + 28z2)) = 0

Combine like terms: 36z + -42z = -6z
(-54 + -6z + 28z2) = 0

Solving
-54 + -6z + 28z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + -3z + 14z2) = 0

Factor a trinomial.
2((-9 + -7z)(3 + -2z)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -7z)' equal to zero and attempt to solve:

Simplifying
-9 + -7z = 0

Solving
-9 + -7z = 0

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

Add '9' to each side of the equation.
-9 + 9 + -7z = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -7z = 0 + 9
-7z = 0 + 9

Combine like terms: 0 + 9 = 9
-7z = 9

Divide each side by '-7'.
z = -1.285714286

Simplifying
z = -1.285714286
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 = {-1.285714286, 1.5}