(7-z)(3z-5)=0

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Solution for (7-z)(3z-5)=0 equation: 


Simplifying
(7 + -1z)(3z + -5) = 0

Reorder the terms:
(7 + -1z)(-5 + 3z) = 0

Multiply (7 + -1z) * (-5 + 3z)
(7(-5 + 3z) + -1z * (-5 + 3z)) = 0
((-5 * 7 + 3z * 7) + -1z * (-5 + 3z)) = 0
((-35 + 21z) + -1z * (-5 + 3z)) = 0
(-35 + 21z + (-5 * -1z + 3z * -1z)) = 0
(-35 + 21z + (5z + -3z2)) = 0

Combine like terms: 21z + 5z = 26z
(-35 + 26z + -3z2) = 0

Solving
-35 + 26z + -3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-7 + z)(5 + -3z) = 0


Subproblem 1
Set the factor '(-7 + z)' equal to zero and attempt to solve:

Simplifying
-7 + z = 0

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

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

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

Simplifying
z = 7

Subproblem 2
Set the factor '(5 + -3z)' equal to zero and attempt to solve:

Simplifying
5 + -3z = 0

Solving
5 + -3z = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3z = 0 + -5
-3z = 0 + -5

Combine like terms: 0 + -5 = -5
-3z = -5

Divide each side by '-3'.
z = 1.666666667

Simplifying
z = 1.666666667
Solution
z = {7, 1.666666667}

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