3z(2z+1)(5z-4)=

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Solution for 3z(2z+1)(5z-4)= equation:


Simplifying
3z(2z + 1)(5z + -4) = 0

Reorder the terms:
3z(1 + 2z)(5z + -4) = 0

Reorder the terms:
3z(1 + 2z)(-4 + 5z) = 0

Multiply (1 + 2z) * (-4 + 5z)
3z(1(-4 + 5z) + 2z * (-4 + 5z)) = 0
3z((-4 * 1 + 5z * 1) + 2z * (-4 + 5z)) = 0
3z((-4 + 5z) + 2z * (-4 + 5z)) = 0
3z(-4 + 5z + (-4 * 2z + 5z * 2z)) = 0
3z(-4 + 5z + (-8z + 10z2)) = 0

Combine like terms: 5z + -8z = -3z
3z(-4 + -3z + 10z2) = 0
(-4 * 3z + -3z * 3z + 10z2 * 3z) = 0
(-12z + -9z2 + 30z3) = 0

Solving
-12z + -9z2 + 30z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3z'.
3z(-4 + -3z + 10z2) = 0

Factor a trinomial.
3z((-1 + -2z)(4 + -5z)) = 0

Ignore the factor 3.

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 '(4 + -5z)' equal to zero and attempt to solve: Simplifying 4 + -5z = 0 Solving 4 + -5z = 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 + -5z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5z = 0 + -4 -5z = 0 + -4 Combine like terms: 0 + -4 = -4 -5z = -4 Divide each side by '-5'. z = 0.8 Simplifying z = 0.8

Solution

z = {0, -0.5, 0.8}

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