(x-5)(2x+7)(3x)=0

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Solution for (x-5)(2x+7)(3x)=0 equation: 


Simplifying
(x + -5)(2x + 7)(3x) = 0

Reorder the terms:
(-5 + x)(2x + 7)(3x) = 0

Reorder the terms:
(-5 + x)(7 + 2x)(3x) = 0

Remove parenthesis around (3x)
(-5 + x)(7 + 2x) * 3x = 0

Reorder the terms for easier multiplication:
3x(-5 + x)(7 + 2x) = 0

Multiply (-5 + x) * (7 + 2x)
3x(-5(7 + 2x) + x(7 + 2x)) = 0
3x((7 * -5 + 2x * -5) + x(7 + 2x)) = 0
3x((-35 + -10x) + x(7 + 2x)) = 0
3x(-35 + -10x + (7 * x + 2x * x)) = 0
3x(-35 + -10x + (7x + 2x2)) = 0

Combine like terms: -10x + 7x = -3x
3x(-35 + -3x + 2x2) = 0
(-35 * 3x + -3x * 3x + 2x2 * 3x) = 0
(-105x + -9x2 + 6x3) = 0

Solving
-105x + -9x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-35 + -3x + 2x2) = 0

Factor a trinomial.
3x((-7 + -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 '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

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, -3.5, 5}

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