(4z-7)(8+z)=0

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Solution for (4z-7)(8+z)=0 equation: 


Simplifying
(4z + -7)(8 + z) = 0

Reorder the terms:
(-7 + 4z)(8 + z) = 0

Multiply (-7 + 4z) * (8 + z)
(-7(8 + z) + 4z * (8 + z)) = 0
((8 * -7 + z * -7) + 4z * (8 + z)) = 0
((-56 + -7z) + 4z * (8 + z)) = 0
(-56 + -7z + (8 * 4z + z * 4z)) = 0
(-56 + -7z + (32z + 4z2)) = 0

Combine like terms: -7z + 32z = 25z
(-56 + 25z + 4z2) = 0

Solving
-56 + 25z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-8 + -1z)(7 + -4z) = 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 '(7 + -4z)' equal to zero and attempt to solve:

Simplifying
7 + -4z = 0

Solving
7 + -4z = 0

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

Add '-7' to each side of the equation.
7 + -7 + -4z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4z = 0 + -7
-4z = 0 + -7

Combine like terms: 0 + -7 = -7
-4z = -7

Divide each side by '-4'.
z = 1.75

Simplifying
z = 1.75
Solution
z = {-8, 1.75}

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