(7+z)(2z-1)=0

Solution for (7+z)(2z-1)=0 equation:

Simplifying
(7 + z)(2z + -1) = 0

Reorder the terms:
(7 + z)(-1 + 2z) = 0

Multiply (7 + z) * (-1 + 2z)
(7(-1 + 2z) + z(-1 + 2z)) = 0
((-1 * 7 + 2z * 7) + z(-1 + 2z)) = 0
((-7 + 14z) + z(-1 + 2z)) = 0
(-7 + 14z + (-1 * z + 2z * z)) = 0
(-7 + 14z + (-1z + 2z2)) = 0

Combine like terms: 14z + -1z = 13z
(-7 + 13z + 2z2) = 0

Solving
-7 + 13z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-7 + -1z)(1 + -2z) = 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 + -2z)' equal to zero and attempt to solve:

Simplifying
1 + -2z = 0

Solving
1 + -2z = 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 + -2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2z = 0 + -1
-2z = 0 + -1

Combine like terms: 0 + -1 = -1
-2z = -1

Divide each side by '-2'.
z = 0.5

Simplifying
z = 0.5
Solution
z = {-7, 0.5}