X(3X+1)(5X-2)=0

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Solution for X(3X+1)(5X-2)=0 equation: 


Simplifying
X(3X + 1)(5X + -2) = 0

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

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

Multiply (1 + 3X) * (-2 + 5X)
X(1(-2 + 5X) + 3X * (-2 + 5X)) = 0
X((-2 * 1 + 5X * 1) + 3X * (-2 + 5X)) = 0
X((-2 + 5X) + 3X * (-2 + 5X)) = 0
X(-2 + 5X + (-2 * 3X + 5X * 3X)) = 0
X(-2 + 5X + (-6X + 15X2)) = 0

Combine like terms: 5X + -6X = -1X
X(-2 + -1X + 15X2) = 0
(-2 * X + -1X * X + 15X2 * X) = 0
(-2X + -1X2 + 15X3) = 0

Solving
-2X + -1X2 + 15X3 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), 'X'.
X(-2 + -1X + 15X2) = 0

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


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 + -3X)' equal to zero and attempt to solve:

Simplifying
-1 + -3X = 0

Solving
-1 + -3X = 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 + -3X = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3X = 0 + 1
-3X = 0 + 1

Combine like terms: 0 + 1 = 1
-3X = 1

Divide each side by '-3'.
X = -0.3333333333

Simplifying
X = -0.3333333333

Subproblem 3
Set the factor '(2 + -5X)' equal to zero and attempt to solve:

Simplifying
2 + -5X = 0

Solving
2 + -5X = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5X = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5X = 0 + -2
-5X = 0 + -2

Combine like terms: 0 + -2 = -2
-5X = -2

Divide each side by '-5'.
X = 0.4

Simplifying
X = 0.4
Solution
X = {0, -0.3333333333, 0.4}

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