(z-5)2z=7(5-z)

Solution for (z-5)2z=7(5-z) equation:

Simplifying
(z + -5) * 2z = 7(5 + -1z)

Reorder the terms:
(-5 + z) * 2z = 7(5 + -1z)

Reorder the terms for easier multiplication:
2z(-5 + z) = 7(5 + -1z)
(-5 * 2z + z * 2z) = 7(5 + -1z)
(-10z + 2z2) = 7(5 + -1z)
-10z + 2z2 = (5 * 7 + -1z * 7)
-10z + 2z2 = (35 + -7z)

Solving
-10z + 2z2 = 35 + -7z

Solving for variable 'z'.

Reorder the terms:
-35 + -10z + 7z + 2z2 = 35 + -7z + -35 + 7z

Combine like terms: -10z + 7z = -3z
-35 + -3z + 2z2 = 35 + -7z + -35 + 7z

Reorder the terms:
-35 + -3z + 2z2 = 35 + -35 + -7z + 7z

Combine like terms: 35 + -35 = 0
-35 + -3z + 2z2 = 0 + -7z + 7z
-35 + -3z + 2z2 = -7z + 7z

Combine like terms: -7z + 7z = 0
-35 + -3z + 2z2 = 0

Factor a trinomial.
(-7 + -2z)(5 + -1z) = 0

Subproblem 1
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
Subproblem 2
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
Solution
z = {-3.5, 5}