z^2+36=13z

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Solution for z^2+36=13z equation:


Simplifying
z2 + 36 = 13z

Reorder the terms:
36 + z2 = 13z

Solving
36 + z2 = 13z

Solving for variable 'z'.

Reorder the terms:
36 + -13z + z2 = 13z + -13z

Combine like terms: 13z + -13z = 0
36 + -13z + z2 = 0

Factor a trinomial.
(4 + -1z)(9 + -1z) = 0

Subproblem 1

Set the factor '(4 + -1z)' equal to zero and attempt to solve: Simplifying 4 + -1z = 0 Solving 4 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1z = 0 + -4 -1z = 0 + -4 Combine like terms: 0 + -4 = -4 -1z = -4 Divide each side by '-1'. z = 4 Simplifying z = 4

Subproblem 2

Set the factor '(9 + -1z)' equal to zero and attempt to solve: Simplifying 9 + -1z = 0 Solving 9 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1z = 0 + -9 -1z = 0 + -9 Combine like terms: 0 + -9 = -9 -1z = -9 Divide each side by '-1'. z = 9 Simplifying z = 9

Solution

z = {4, 9}

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