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

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Solution for (2-z)(5z-7)=0 equation: 


Simplifying
(2 + -1z)(5z + -7) = 0

Reorder the terms:
(2 + -1z)(-7 + 5z) = 0

Multiply (2 + -1z) * (-7 + 5z)
(2(-7 + 5z) + -1z * (-7 + 5z)) = 0
((-7 * 2 + 5z * 2) + -1z * (-7 + 5z)) = 0
((-14 + 10z) + -1z * (-7 + 5z)) = 0
(-14 + 10z + (-7 * -1z + 5z * -1z)) = 0
(-14 + 10z + (7z + -5z2)) = 0

Combine like terms: 10z + 7z = 17z
(-14 + 17z + -5z2) = 0

Solving
-14 + 17z + -5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-2 + z)(7 + -5z) = 0


Subproblem 1
Set the factor '(-2 + z)' equal to zero and attempt to solve:

Simplifying
-2 + z = 0

Solving
-2 + z = 0

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

Add '2' to each side of the equation.
-2 + 2 + z = 0 + 2

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

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

Simplifying
z = 2

Subproblem 2
Set the factor '(7 + -5z)' equal to zero and attempt to solve:

Simplifying
7 + -5z = 0

Solving
7 + -5z = 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 + -5z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5z = 0 + -7
-5z = 0 + -7

Combine like terms: 0 + -7 = -7
-5z = -7

Divide each side by '-5'.
z = 1.4

Simplifying
z = 1.4
Solution
z = {2, 1.4}

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