(21x^2-35x)(-6x+10)=0

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Solution for (21x^2-35x)(-6x+10)=0 equation: 


Simplifying
(21x2 + -35x)(-6x + 10) = 0

Reorder the terms:
(-35x + 21x2)(-6x + 10) = 0

Reorder the terms:
(-35x + 21x2)(10 + -6x) = 0

Multiply (-35x + 21x2) * (10 + -6x)
(-35x * (10 + -6x) + 21x2 * (10 + -6x)) = 0
((10 * -35x + -6x * -35x) + 21x2 * (10 + -6x)) = 0
((-350x + 210x2) + 21x2 * (10 + -6x)) = 0
(-350x + 210x2 + (10 * 21x2 + -6x * 21x2)) = 0
(-350x + 210x2 + (210x2 + -126x3)) = 0

Combine like terms: 210x2 + 210x2 = 420x2
(-350x + 420x2 + -126x3) = 0

Solving
-350x + 420x2 + -126x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '14x'.
14x(-25 + 30x + -9x2) = 0

Factor a trinomial.
14x((-5 + 3x)(5 + -3x)) = 0

Ignore the factor 14.

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 + 3x)' equal to zero and attempt to solve:

Simplifying
-5 + 3x = 0

Solving
-5 + 3x = 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 + 3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 3x = 0 + 5
3x = 0 + 5

Combine like terms: 0 + 5 = 5
3x = 5

Divide each side by '3'.
x = 1.666666667

Simplifying
x = 1.666666667

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

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {0, 1.666666667, 1.666666667}

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