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

Solution for (7+z)(5z-1)=0 equation:

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

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

Multiply (7 + z) * (-1 + 5z)
(7(-1 + 5z) + z(-1 + 5z)) = 0
((-1 * 7 + 5z * 7) + z(-1 + 5z)) = 0
((-7 + 35z) + z(-1 + 5z)) = 0
(-7 + 35z + (-1 * z + 5z * z)) = 0
(-7 + 35z + (-1z + 5z2)) = 0

Combine like terms: 35z + -1z = 34z
(-7 + 34z + 5z2) = 0

Solving
-7 + 34z + 5z2 = 0

Solving for variable 'z'.

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

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

Simplifying
-7 + -1z = 0

Solving
-7 + -1z = 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 + -1z = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1z = 0 + 7
-1z = 0 + 7

Combine like terms: 0 + 7 = 7
-1z = 7

Divide each side by '-1'.
z = -7

Simplifying
z = -7
Subproblem 2
Set the factor '(1 + -5z)' equal to zero and attempt to solve:

Simplifying
1 + -5z = 0

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

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

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

Divide each side by '-5'.
z = 0.2

Simplifying
z = 0.2
Solution
z = {-7, 0.2}