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

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


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

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

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