3x(4x^2-19x-5)=0

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Solution for 3x(4x^2-19x-5)=0 equation:


Simplifying
3x(4x2 + -19x + -5) = 0

Reorder the terms:
3x(-5 + -19x + 4x2) = 0
(-5 * 3x + -19x * 3x + 4x2 * 3x) = 0
(-15x + -57x2 + 12x3) = 0

Solving
-15x + -57x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-5 + -19x + 4x2) = 0

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

Ignore the factor 3.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(-1 + -4x)' equal to zero and attempt to solve: Simplifying -1 + -4x = 0 Solving -1 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -4x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4x = 0 + 1 -4x = 0 + 1 Combine like terms: 0 + 1 = 1 -4x = 1 Divide each side by '-4'. x = -0.25 Simplifying x = -0.25

Subproblem 3

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {0, -0.25, 5}

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