4z^2(2z+9)(9z-2)=0

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Solution for 4z^2(2z+9)(9z-2)=0 equation: 


Simplifying
4z2(2z + 9)(9z + -2) = 0

Reorder the terms:
4z2(9 + 2z)(9z + -2) = 0

Reorder the terms:
4z2(9 + 2z)(-2 + 9z) = 0

Multiply (9 + 2z) * (-2 + 9z)
4z2(9(-2 + 9z) + 2z * (-2 + 9z)) = 0
4z2((-2 * 9 + 9z * 9) + 2z * (-2 + 9z)) = 0
4z2((-18 + 81z) + 2z * (-2 + 9z)) = 0
4z2(-18 + 81z + (-2 * 2z + 9z * 2z)) = 0
4z2(-18 + 81z + (-4z + 18z2)) = 0

Combine like terms: 81z + -4z = 77z
4z2(-18 + 77z + 18z2) = 0
(-18 * 4z2 + 77z * 4z2 + 18z2 * 4z2) = 0
(-72z2 + 308z3 + 72z4) = 0

Solving
-72z2 + 308z3 + 72z4 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4z2'.
4z2(-18 + 77z + 18z2) = 0

Factor a trinomial.
4z2((-9 + -2z)(2 + -9z)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve:

Simplifying
z2 = 0

Solving
z2 = 0

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

Simplifying
z2 = 0

Take the square root of each side:
z = {0}

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

Simplifying
-9 + -2z = 0

Solving
-9 + -2z = 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 + -2z = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2z = 0 + 9
-2z = 0 + 9

Combine like terms: 0 + 9 = 9
-2z = 9

Divide each side by '-2'.
z = -4.5

Simplifying
z = -4.5

Subproblem 3
Set the factor '(2 + -9z)' equal to zero and attempt to solve:

Simplifying
2 + -9z = 0

Solving
2 + -9z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -9z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -9z = 0 + -2
-9z = 0 + -2

Combine like terms: 0 + -2 = -2
-9z = -2

Divide each side by '-9'.
z = 0.2222222222

Simplifying
z = 0.2222222222
Solution
z = {0, -4.5, 0.2222222222}

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