21z^2=85z-26

Solution for 21z^2=85z-26 equation:

Simplifying
21z2 = 85z + -26

Reorder the terms:
21z2 = -26 + 85z

Solving
21z2 = -26 + 85z

Solving for variable 'z'.

Reorder the terms:
26 + -85z + 21z2 = -26 + 85z + 26 + -85z

Reorder the terms:
26 + -85z + 21z2 = -26 + 26 + 85z + -85z

Combine like terms: -26 + 26 = 0
26 + -85z + 21z2 = 0 + 85z + -85z
26 + -85z + 21z2 = 85z + -85z

Combine like terms: 85z + -85z = 0
26 + -85z + 21z2 = 0

Factor a trinomial.
(1 + -3z)(26 + -7z) = 0

Subproblem 1
Set the factor '(1 + -3z)' equal to zero and attempt to solve:

Simplifying
1 + -3z = 0

Solving
1 + -3z = 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 + -3z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3z = 0 + -1
-3z = 0 + -1

Combine like terms: 0 + -1 = -1
-3z = -1

Divide each side by '-3'.
z = 0.3333333333

Simplifying
z = 0.3333333333
Subproblem 2
Set the factor '(26 + -7z)' equal to zero and attempt to solve:

Simplifying
26 + -7z = 0

Solving
26 + -7z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-26' to each side of the equation.
26 + -26 + -7z = 0 + -26

Combine like terms: 26 + -26 = 0
0 + -7z = 0 + -26
-7z = 0 + -26

Combine like terms: 0 + -26 = -26
-7z = -26

Divide each side by '-7'.
z = 3.714285714

Simplifying
z = 3.714285714
Solution
z = {0.3333333333, 3.714285714}