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

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


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

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

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

Combine like terms: 24z + -4z = 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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