(x+5)(3x-2)(23x)=0

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Solution for (x+5)(3x-2)(23x)=0 equation: 


Simplifying
(x + 5)(3x + -2)(23x) = 0

Reorder the terms:
(5 + x)(3x + -2)(23x) = 0

Reorder the terms:
(5 + x)(-2 + 3x)(23x) = 0

Remove parenthesis around (23x)
(5 + x)(-2 + 3x) * 23x = 0

Reorder the terms for easier multiplication:
23x(5 + x)(-2 + 3x) = 0

Multiply (5 + x) * (-2 + 3x)
23x(5(-2 + 3x) + x(-2 + 3x)) = 0
23x((-2 * 5 + 3x * 5) + x(-2 + 3x)) = 0
23x((-10 + 15x) + x(-2 + 3x)) = 0
23x(-10 + 15x + (-2 * x + 3x * x)) = 0
23x(-10 + 15x + (-2x + 3x2)) = 0

Combine like terms: 15x + -2x = 13x
23x(-10 + 13x + 3x2) = 0
(-10 * 23x + 13x * 23x + 3x2 * 23x) = 0
(-230x + 299x2 + 69x3) = 0

Solving
-230x + 299x2 + 69x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '23x'.
23x(-10 + 13x + 3x2) = 0

Factor a trinomial.
23x((-5 + -1x)(2 + -3x)) = 0

Ignore the factor 23.

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 '(-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

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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {0, -5, 0.6666666667}

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