(9+z)(4z-7)=0

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Solution for (9+z)(4z-7)=0 equation: 


Simplifying
(9 + z)(4z + -7) = 0

Reorder the terms:
(9 + z)(-7 + 4z) = 0

Multiply (9 + z) * (-7 + 4z)
(9(-7 + 4z) + z(-7 + 4z)) = 0
((-7 * 9 + 4z * 9) + z(-7 + 4z)) = 0
((-63 + 36z) + z(-7 + 4z)) = 0
(-63 + 36z + (-7 * z + 4z * z)) = 0
(-63 + 36z + (-7z + 4z2)) = 0

Combine like terms: 36z + -7z = 29z
(-63 + 29z + 4z2) = 0

Solving
-63 + 29z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-9 + -1z)(7 + -4z) = 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 + -4z)' equal to zero and attempt to solve:

Simplifying
7 + -4z = 0

Solving
7 + -4z = 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 + -4z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4z = 0 + -7
-4z = 0 + -7

Combine like terms: 0 + -7 = -7
-4z = -7

Divide each side by '-4'.
z = 1.75

Simplifying
z = 1.75
Solution
z = {-9, 1.75}

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