(4z+5)(9z+8)=0

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Solution for (4z+5)(9z+8)=0 equation: 


Simplifying
(4z + 5)(9z + 8) = 0

Reorder the terms:
(5 + 4z)(9z + 8) = 0

Reorder the terms:
(5 + 4z)(8 + 9z) = 0

Multiply (5 + 4z) * (8 + 9z)
(5(8 + 9z) + 4z * (8 + 9z)) = 0
((8 * 5 + 9z * 5) + 4z * (8 + 9z)) = 0
((40 + 45z) + 4z * (8 + 9z)) = 0
(40 + 45z + (8 * 4z + 9z * 4z)) = 0
(40 + 45z + (32z + 36z2)) = 0

Combine like terms: 45z + 32z = 77z
(40 + 77z + 36z2) = 0

Solving
40 + 77z + 36z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(5 + 4z)(8 + 9z) = 0


Subproblem 1
Set the factor '(5 + 4z)' equal to zero and attempt to solve:

Simplifying
5 + 4z = 0

Solving
5 + 4z = 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 + 4z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4z = 0 + -5
4z = 0 + -5

Combine like terms: 0 + -5 = -5
4z = -5

Divide each side by '4'.
z = -1.25

Simplifying
z = -1.25

Subproblem 2
Set the factor '(8 + 9z)' equal to zero and attempt to solve:

Simplifying
8 + 9z = 0

Solving
8 + 9z = 0

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

Add '-8' to each side of the equation.
8 + -8 + 9z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 9z = 0 + -8
9z = 0 + -8

Combine like terms: 0 + -8 = -8
9z = -8

Divide each side by '9'.
z = -0.8888888889

Simplifying
z = -0.8888888889
Solution
z = {-1.25, -0.8888888889}

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