4z(4z+2)(5z-6)=0

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Solution for 4z(4z+2)(5z-6)=0 equation:


Simplifying
4z(4z + 2)(5z + -6) = 0

Reorder the terms:
4z(2 + 4z)(5z + -6) = 0

Reorder the terms:
4z(2 + 4z)(-6 + 5z) = 0

Multiply (2 + 4z) * (-6 + 5z)
4z(2(-6 + 5z) + 4z * (-6 + 5z)) = 0
4z((-6 * 2 + 5z * 2) + 4z * (-6 + 5z)) = 0
4z((-12 + 10z) + 4z * (-6 + 5z)) = 0
4z(-12 + 10z + (-6 * 4z + 5z * 4z)) = 0
4z(-12 + 10z + (-24z + 20z2)) = 0

Combine like terms: 10z + -24z = -14z
4z(-12 + -14z + 20z2) = 0
(-12 * 4z + -14z * 4z + 20z2 * 4z) = 0
(-48z + -56z2 + 80z3) = 0

Solving
-48z + -56z2 + 80z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '8z'.
8z(-6 + -7z + 10z2) = 0

Factor a trinomial.
8z((-1 + -2z)(6 + -5z)) = 0

Ignore the factor 8.

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 '(-1 + -2z)' equal to zero and attempt to solve: Simplifying -1 + -2z = 0 Solving -1 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2z = 0 + 1 -2z = 0 + 1 Combine like terms: 0 + 1 = 1 -2z = 1 Divide each side by '-2'. z = -0.5 Simplifying z = -0.5

Subproblem 3

Set the factor '(6 + -5z)' equal to zero and attempt to solve: Simplifying 6 + -5z = 0 Solving 6 + -5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5z = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5z = 0 + -6 -5z = 0 + -6 Combine like terms: 0 + -6 = -6 -5z = -6 Divide each side by '-5'. z = 1.2 Simplifying z = 1.2

Solution

z = {0, -0.5, 1.2}

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