(3z-7)(1-z)=0

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Solution for (3z-7)(1-z)=0 equation: 


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

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

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

Combine like terms: 7z + 3z = 10z
(-7 + 10z + -3z2) = 0

Solving
-7 + 10z + -3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-7 + 3z)(1 + -1z) = 0


Subproblem 1
Set the factor '(-7 + 3z)' equal to zero and attempt to solve:

Simplifying
-7 + 3z = 0

Solving
-7 + 3z = 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 + 3z = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 3z = 0 + 7
3z = 0 + 7

Combine like terms: 0 + 7 = 7
3z = 7

Divide each side by '3'.
z = 2.333333333

Simplifying
z = 2.333333333

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

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1z = 0 + -1
-1z = 0 + -1

Combine like terms: 0 + -1 = -1
-1z = -1

Divide each side by '-1'.
z = 1

Simplifying
z = 1
Solution
z = {2.333333333, 1}

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