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

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


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

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

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

Multiply (2 + X) * (-5 + 2X)
3X(2(-5 + 2X) + X(-5 + 2X)) = 0
3X((-5 * 2 + 2X * 2) + X(-5 + 2X)) = 0
3X((-10 + 4X) + X(-5 + 2X)) = 0
3X(-10 + 4X + (-5 * X + 2X * X)) = 0
3X(-10 + 4X + (-5X + 2X2)) = 0

Combine like terms: 4X + -5X = -1X
3X(-10 + -1X + 2X2) = 0
(-10 * 3X + -1X * 3X + 2X2 * 3X) = 0
(-30X + -3X2 + 6X3) = 0

Solving
-30X + -3X2 + 6X3 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '3X'.
3X(-10 + -1X + 2X2) = 0

Factor a trinomial.
3X((-2 + -1X)(5 + -2X)) = 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 '(-2 + -1X)' equal to zero and attempt to solve:

Simplifying
-2 + -1X = 0

Solving
-2 + -1X = 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 + -1X = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1X = 0 + 2
-1X = 0 + 2

Combine like terms: 0 + 2 = 2
-1X = 2

Divide each side by '-1'.
X = -2

Simplifying
X = -2

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

Simplifying
5 + -2X = 0

Solving
5 + -2X = 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 + -2X = 0 + -5

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

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

Divide each side by '-2'.
X = 2.5

Simplifying
X = 2.5
Solution
X = {0, -2, 2.5}

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