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

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


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

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

Multiply (3 + -7x) * (5 + 2x)
x(3(5 + 2x) + -7x * (5 + 2x)) = 0
x((5 * 3 + 2x * 3) + -7x * (5 + 2x)) = 0
x((15 + 6x) + -7x * (5 + 2x)) = 0
x(15 + 6x + (5 * -7x + 2x * -7x)) = 0
x(15 + 6x + (-35x + -14x2)) = 0

Combine like terms: 6x + -35x = -29x
x(15 + -29x + -14x2) = 0
(15 * x + -29x * x + -14x2 * x) = 0
(15x + -29x2 + -14x3) = 0

Solving
15x + -29x2 + -14x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(15 + -29x + -14x2) = 0

Factor a trinomial.
x((3 + -7x)(5 + 2x)) = 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 '(3 + -7x)' equal to zero and attempt to solve:

Simplifying
3 + -7x = 0

Solving
3 + -7x = 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 + -7x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7x = 0 + -3
-7x = 0 + -3

Combine like terms: 0 + -3 = -3
-7x = -3

Divide each side by '-7'.
x = 0.4285714286

Simplifying
x = 0.4285714286

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, 0.4285714286, -2.5}

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