(3z-4)(8+z)=0

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Solution for (3z-4)(8+z)=0 equation: 


Simplifying
(3z + -4)(8 + z) = 0

Reorder the terms:
(-4 + 3z)(8 + z) = 0

Multiply (-4 + 3z) * (8 + z)
(-4(8 + z) + 3z * (8 + z)) = 0
((8 * -4 + z * -4) + 3z * (8 + z)) = 0
((-32 + -4z) + 3z * (8 + z)) = 0
(-32 + -4z + (8 * 3z + z * 3z)) = 0
(-32 + -4z + (24z + 3z2)) = 0

Combine like terms: -4z + 24z = 20z
(-32 + 20z + 3z2) = 0

Solving
-32 + 20z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-8 + -1z)(4 + -3z) = 0


Subproblem 1
Set the factor '(-8 + -1z)' equal to zero and attempt to solve:

Simplifying
-8 + -1z = 0

Solving
-8 + -1z = 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 + -1z = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1z = 0 + 8
-1z = 0 + 8

Combine like terms: 0 + 8 = 8
-1z = 8

Divide each side by '-1'.
z = -8

Simplifying
z = -8

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

Simplifying
4 + -3z = 0

Solving
4 + -3z = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3z = 0 + -4

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

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

Divide each side by '-3'.
z = 1.333333333

Simplifying
z = 1.333333333
Solution
z = {-8, 1.333333333}

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