2z^2+11z+17=z^2+22z-11

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Solution for 2z^2+11z+17=z^2+22z-11 equation: 


Simplifying
2z2 + 11z + 17 = z2 + 22z + -11

Reorder the terms:
17 + 11z + 2z2 = z2 + 22z + -11

Reorder the terms:
17 + 11z + 2z2 = -11 + 22z + z2

Solving
17 + 11z + 2z2 = -11 + 22z + z2

Solving for variable 'z'.

Reorder the terms:
17 + 11 + 11z + -22z + 2z2 + -1z2 = -11 + 22z + z2 + 11 + -22z + -1z2

Combine like terms: 17 + 11 = 28
28 + 11z + -22z + 2z2 + -1z2 = -11 + 22z + z2 + 11 + -22z + -1z2

Combine like terms: 11z + -22z = -11z
28 + -11z + 2z2 + -1z2 = -11 + 22z + z2 + 11 + -22z + -1z2

Combine like terms: 2z2 + -1z2 = 1z2
28 + -11z + 1z2 = -11 + 22z + z2 + 11 + -22z + -1z2

Reorder the terms:
28 + -11z + 1z2 = -11 + 11 + 22z + -22z + z2 + -1z2

Combine like terms: -11 + 11 = 0
28 + -11z + 1z2 = 0 + 22z + -22z + z2 + -1z2
28 + -11z + 1z2 = 22z + -22z + z2 + -1z2

Combine like terms: 22z + -22z = 0
28 + -11z + 1z2 = 0 + z2 + -1z2
28 + -11z + 1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
28 + -11z + 1z2 = 0

Factor a trinomial.
(4 + -1z)(7 + -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 '(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 = {4, 7}

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