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

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


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

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

Multiply (5 + z) * (-7 + 3z)
(5(-7 + 3z) + z(-7 + 3z)) = 0
((-7 * 5 + 3z * 5) + z(-7 + 3z)) = 0
((-35 + 15z) + z(-7 + 3z)) = 0
(-35 + 15z + (-7 * z + 3z * z)) = 0
(-35 + 15z + (-7z + 3z2)) = 0

Combine like terms: 15z + -7z = 8z
(-35 + 8z + 3z2) = 0

Solving
-35 + 8z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-5 + -1z)(7 + -3z) = 0


Subproblem 1
Set the factor '(-5 + -1z)' equal to zero and attempt to solve:

Simplifying
-5 + -1z = 0

Solving
-5 + -1z = 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 + -1z = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1z = 0 + 5
-1z = 0 + 5

Combine like terms: 0 + 5 = 5
-1z = 5

Divide each side by '-1'.
z = -5

Simplifying
z = -5

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 = {-5, 2.333333333}

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