7z(8z+9)(z-9)=0

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Solution for 7z(8z+9)(z-9)=0 equation: 


Simplifying
7z(8z + 9)(z + -9) = 0

Reorder the terms:
7z(9 + 8z)(z + -9) = 0

Reorder the terms:
7z(9 + 8z)(-9 + z) = 0

Multiply (9 + 8z) * (-9 + z)
7z(9(-9 + z) + 8z * (-9 + z)) = 0
7z((-9 * 9 + z * 9) + 8z * (-9 + z)) = 0
7z((-81 + 9z) + 8z * (-9 + z)) = 0
7z(-81 + 9z + (-9 * 8z + z * 8z)) = 0
7z(-81 + 9z + (-72z + 8z2)) = 0

Combine like terms: 9z + -72z = -63z
7z(-81 + -63z + 8z2) = 0
(-81 * 7z + -63z * 7z + 8z2 * 7z) = 0
(-567z + -441z2 + 56z3) = 0

Solving
-567z + -441z2 + 56z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '7z'.
7z(-81 + -63z + 8z2) = 0

Factor a trinomial.
7z((-9 + -8z)(9 + -1z)) = 0

Ignore the factor 7.

Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

Move all terms containing z to the left, all other terms to the right.

Simplifying
z = 0

Subproblem 2
Set the factor '(-9 + -8z)' equal to zero and attempt to solve:

Simplifying
-9 + -8z = 0

Solving
-9 + -8z = 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 + -8z = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -8z = 0 + 9
-8z = 0 + 9

Combine like terms: 0 + 9 = 9
-8z = 9

Divide each side by '-8'.
z = -1.125

Simplifying
z = -1.125

Subproblem 3
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
Solution
z = {0, -1.125, 9}

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