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

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

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

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

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

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

Combine like terms: -2z + -7z = -9z
(7 + -9z + 2z2) = 0

Solving
7 + -9z + 2z2 = 0

Solving for variable 'z'.

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

Simplifying
7 + -2z = 0

Solving
7 + -2z = 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 + -2z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2z = 0 + -7
-2z = 0 + -7

Combine like terms: 0 + -7 = -7
-2z = -7

Divide each side by '-2'.
z = 3.5

Simplifying
z = 3.5
Solution
z = {1, 3.5}