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

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


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

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

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

Multiply (3 + 2x) * (-5 + x)
3x(3(-5 + x) + 2x * (-5 + x)) = 0
3x((-5 * 3 + x * 3) + 2x * (-5 + x)) = 0
3x((-15 + 3x) + 2x * (-5 + x)) = 0
3x(-15 + 3x + (-5 * 2x + x * 2x)) = 0
3x(-15 + 3x + (-10x + 2x2)) = 0

Combine like terms: 3x + -10x = -7x
3x(-15 + -7x + 2x2) = 0
(-15 * 3x + -7x * 3x + 2x2 * 3x) = 0
(-45x + -21x2 + 6x3) = 0

Solving
-45x + -21x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-15 + -7x + 2x2) = 0

Factor a trinomial.
3x((-3 + -2x)(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 '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

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, -1.5, 5}

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