(2z+7)(9-z)=0

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Solution for (2z+7)(9-z)=0 equation: 


Simplifying
(2z + 7)(9 + -1z) = 0

Reorder the terms:
(7 + 2z)(9 + -1z) = 0

Multiply (7 + 2z) * (9 + -1z)
(7(9 + -1z) + 2z * (9 + -1z)) = 0
((9 * 7 + -1z * 7) + 2z * (9 + -1z)) = 0
((63 + -7z) + 2z * (9 + -1z)) = 0
(63 + -7z + (9 * 2z + -1z * 2z)) = 0
(63 + -7z + (18z + -2z2)) = 0

Combine like terms: -7z + 18z = 11z
(63 + 11z + -2z2) = 0

Solving
63 + 11z + -2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(9 + -1z)(7 + 2z) = 0


Subproblem 1
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

Subproblem 2
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
Solution
z = {9, -3.5}

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