(8+z)(2z-7)=0

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Solution for (8+z)(2z-7)=0 equation: 


Simplifying
(8 + z)(2z + -7) = 0

Reorder the terms:
(8 + z)(-7 + 2z) = 0

Multiply (8 + z) * (-7 + 2z)
(8(-7 + 2z) + z(-7 + 2z)) = 0
((-7 * 8 + 2z * 8) + z(-7 + 2z)) = 0
((-56 + 16z) + z(-7 + 2z)) = 0
(-56 + 16z + (-7 * z + 2z * z)) = 0
(-56 + 16z + (-7z + 2z2)) = 0

Combine like terms: 16z + -7z = 9z
(-56 + 9z + 2z2) = 0

Solving
-56 + 9z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-8 + -1z)(7 + -2z) = 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 + -2z)' equal to zero and attempt to solve:

Simplifying
7 + -2z = 0

Solving
7 + -2z = 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 + -2z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2z = 0 + -7
-2z = 0 + -7

Combine like terms: 0 + -7 = -7
-2z = -7

Divide each side by '-2'.
z = 3.5

Simplifying
z = 3.5
Solution
z = {-8, 3.5}

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