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

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


Simplifying
(4 + -1z)(3z + 8) = 0

Reorder the terms:
(4 + -1z)(8 + 3z) = 0

Multiply (4 + -1z) * (8 + 3z)
(4(8 + 3z) + -1z * (8 + 3z)) = 0
((8 * 4 + 3z * 4) + -1z * (8 + 3z)) = 0
((32 + 12z) + -1z * (8 + 3z)) = 0
(32 + 12z + (8 * -1z + 3z * -1z)) = 0
(32 + 12z + (-8z + -3z2)) = 0

Combine like terms: 12z + -8z = 4z
(32 + 4z + -3z2) = 0

Solving
32 + 4z + -3z2 = 0

Solving for variable 'z'.

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


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

Simplifying
4 + -1z = 0

Solving
4 + -1z = 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 + -1z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1z = 0 + -4
-1z = 0 + -4

Combine like terms: 0 + -4 = -4
-1z = -4

Divide each side by '-1'.
z = 4

Simplifying
z = 4

Subproblem 2
Set the factor '(8 + 3z)' equal to zero and attempt to solve:

Simplifying
8 + 3z = 0

Solving
8 + 3z = 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 + 3z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3z = 0 + -8
3z = 0 + -8

Combine like terms: 0 + -8 = -8
3z = -8

Divide each side by '3'.
z = -2.666666667

Simplifying
z = -2.666666667
Solution
z = {4, -2.666666667}

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