4z(10z-3)(z-4)=0

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Solution for 4z(10z-3)(z-4)=0 equation: 


Simplifying
4z(10z + -3)(z + -4) = 0

Reorder the terms:
4z(-3 + 10z)(z + -4) = 0

Reorder the terms:
4z(-3 + 10z)(-4 + z) = 0

Multiply (-3 + 10z) * (-4 + z)
4z(-3(-4 + z) + 10z * (-4 + z)) = 0
4z((-4 * -3 + z * -3) + 10z * (-4 + z)) = 0
4z((12 + -3z) + 10z * (-4 + z)) = 0
4z(12 + -3z + (-4 * 10z + z * 10z)) = 0
4z(12 + -3z + (-40z + 10z2)) = 0

Combine like terms: -3z + -40z = -43z
4z(12 + -43z + 10z2) = 0
(12 * 4z + -43z * 4z + 10z2 * 4z) = 0
(48z + -172z2 + 40z3) = 0

Solving
48z + -172z2 + 40z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4z'.
4z(12 + -43z + 10z2) = 0

Factor a trinomial.
4z((3 + -10z)(4 + -1z)) = 0

Ignore the factor 4.

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 '(3 + -10z)' equal to zero and attempt to solve:

Simplifying
3 + -10z = 0

Solving
3 + -10z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -10z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -10z = 0 + -3
-10z = 0 + -3

Combine like terms: 0 + -3 = -3
-10z = -3

Divide each side by '-10'.
z = 0.3

Simplifying
z = 0.3

Subproblem 3
Set the factor '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1z = 0 + -4
-1z = 0 + -4

Combine like terms: 0 + -4 = -4
-1z = -4

Divide each side by '-1'.
z = 4

Simplifying
z = 4
Solution
z = {0, 0.3, 4}

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