2z+81=(2z+9)(z+2)

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Solution for 2z+81=(2z+9)(z+2) equation: 


Simplifying
2z + 81 = (2z + 9)(z + 2)

Reorder the terms:
81 + 2z = (2z + 9)(z + 2)

Reorder the terms:
81 + 2z = (9 + 2z)(z + 2)

Reorder the terms:
81 + 2z = (9 + 2z)(2 + z)

Multiply (9 + 2z) * (2 + z)
81 + 2z = (9(2 + z) + 2z * (2 + z))
81 + 2z = ((2 * 9 + z * 9) + 2z * (2 + z))
81 + 2z = ((18 + 9z) + 2z * (2 + z))
81 + 2z = (18 + 9z + (2 * 2z + z * 2z))
81 + 2z = (18 + 9z + (4z + 2z2))

Combine like terms: 9z + 4z = 13z
81 + 2z = (18 + 13z + 2z2)

Solving
81 + 2z = 18 + 13z + 2z2

Solving for variable 'z'.

Reorder the terms:
81 + -18 + 2z + -13z + -2z2 = 18 + 13z + 2z2 + -18 + -13z + -2z2

Combine like terms: 81 + -18 = 63
63 + 2z + -13z + -2z2 = 18 + 13z + 2z2 + -18 + -13z + -2z2

Combine like terms: 2z + -13z = -11z
63 + -11z + -2z2 = 18 + 13z + 2z2 + -18 + -13z + -2z2

Reorder the terms:
63 + -11z + -2z2 = 18 + -18 + 13z + -13z + 2z2 + -2z2

Combine like terms: 18 + -18 = 0
63 + -11z + -2z2 = 0 + 13z + -13z + 2z2 + -2z2
63 + -11z + -2z2 = 13z + -13z + 2z2 + -2z2

Combine like terms: 13z + -13z = 0
63 + -11z + -2z2 = 0 + 2z2 + -2z2
63 + -11z + -2z2 = 2z2 + -2z2

Combine like terms: 2z2 + -2z2 = 0
63 + -11z + -2z2 = 0

Factor a trinomial.
(7 + -2z)(9 + z) = 0


Subproblem 1
Set the factor '(7 + -2z)' equal to zero and attempt to solve:

Simplifying
7 + -2z = 0

Solving
7 + -2z = 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 + -2z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2z = 0 + -7
-2z = 0 + -7

Combine like terms: 0 + -7 = -7
-2z = -7

Divide each side by '-2'.
z = 3.5

Simplifying
z = 3.5

Subproblem 2
Set the factor '(9 + z)' equal to zero and attempt to solve:

Simplifying
9 + z = 0

Solving
9 + z = 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 + z = 0 + -9

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

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

Simplifying
z = -9
Solution
z = {3.5, -9}

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