z^2+14=9z

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Solution for z^2+14=9z equation:


Simplifying
z2 + 14 = 9z

Reorder the terms:
14 + z2 = 9z

Solving
14 + z2 = 9z

Solving for variable 'z'.

Reorder the terms:
14 + -9z + z2 = 9z + -9z

Combine like terms: 9z + -9z = 0
14 + -9z + z2 = 0

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

Subproblem 1

Set the factor '(2 + -1z)' equal to zero and attempt to solve: Simplifying 2 + -1z = 0 Solving 2 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1z = 0 + -2 -1z = 0 + -2 Combine like terms: 0 + -2 = -2 -1z = -2 Divide each side by '-1'. z = 2 Simplifying z = 2

Subproblem 2

Set the factor '(7 + -1z)' equal to zero and attempt to solve: Simplifying 7 + -1z = 0 Solving 7 + -1z = 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 + -1z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1z = 0 + -7 -1z = 0 + -7 Combine like terms: 0 + -7 = -7 -1z = -7 Divide each side by '-1'. z = 7 Simplifying z = 7

Solution

z = {2, 7}

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