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

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


Simplifying
(4z + -7)(8 + -1z) = 0

Reorder the terms:
(-7 + 4z)(8 + -1z) = 0

Multiply (-7 + 4z) * (8 + -1z)
(-7(8 + -1z) + 4z * (8 + -1z)) = 0
((8 * -7 + -1z * -7) + 4z * (8 + -1z)) = 0
((-56 + 7z) + 4z * (8 + -1z)) = 0
(-56 + 7z + (8 * 4z + -1z * 4z)) = 0
(-56 + 7z + (32z + -4z2)) = 0

Combine like terms: 7z + 32z = 39z
(-56 + 39z + -4z2) = 0

Solving
-56 + 39z + -4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-8 + z)(7 + -4z) = 0


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

Simplifying
-8 + z = 0

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

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

Combine like terms: 0 + 8 = 8
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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