-65z(z-61)=z+(-61)

Solution for -65z(z-61)=z+(-61) equation:

Simplifying
-65z(z + -61) = z + (-61)

Reorder the terms:
-65z(-61 + z) = z + (-61)
(-61 * -65z + z * -65z) = z + (-61)
(3965z + -65z2) = z + (-61)
3965z + -65z2 = z + -61

Reorder the terms:
3965z + -65z2 = -61 + z

Solving
3965z + -65z2 = -61 + z

Solving for variable 'z'.

Reorder the terms:
61 + 3965z + -1z + -65z2 = -61 + z + 61 + -1z

Combine like terms: 3965z + -1z = 3964z
61 + 3964z + -65z2 = -61 + z + 61 + -1z

Reorder the terms:
61 + 3964z + -65z2 = -61 + 61 + z + -1z

Combine like terms: -61 + 61 = 0
61 + 3964z + -65z2 = 0 + z + -1z
61 + 3964z + -65z2 = z + -1z

Combine like terms: z + -1z = 0
61 + 3964z + -65z2 = 0

Factor a trinomial.
(61 + -1z)(1 + 65z) = 0

Subproblem 1
Set the factor '(61 + -1z)' equal to zero and attempt to solve:

Simplifying
61 + -1z = 0

Solving
61 + -1z = 0

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

Add '-61' to each side of the equation.
61 + -61 + -1z = 0 + -61

Combine like terms: 61 + -61 = 0
0 + -1z = 0 + -61
-1z = 0 + -61

Combine like terms: 0 + -61 = -61
-1z = -61

Divide each side by '-1'.
z = 61

Simplifying
z = 61
Subproblem 2
Set the factor '(1 + 65z)' equal to zero and attempt to solve:

Simplifying
1 + 65z = 0

Solving
1 + 65z = 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 + 65z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 65z = 0 + -1
65z = 0 + -1

Combine like terms: 0 + -1 = -1
65z = -1

Divide each side by '65'.
z = -0.01538461538

Simplifying
z = -0.01538461538
Solution
z = {61, -0.01538461538}