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

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


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

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

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

Combine like terms: 3z + -7z = -4z
(7 + -4z + -3z2) = 0

Solving
7 + -4z + -3z2 = 0

Solving for variable 'z'.

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


Subproblem 1
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

Subproblem 2
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
Solution
z = {1, -2.333333333}

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