(5y^3-2y^2)(-35y+14)=0

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Solution for (5y^3-2y^2)(-35y+14)=0 equation: 


Simplifying
(5y3 + -2y2)(-35y + 14) = 0

Reorder the terms:
(-2y2 + 5y3)(-35y + 14) = 0

Reorder the terms:
(-2y2 + 5y3)(14 + -35y) = 0

Multiply (-2y2 + 5y3) * (14 + -35y)
(-2y2 * (14 + -35y) + 5y3 * (14 + -35y)) = 0
((14 * -2y2 + -35y * -2y2) + 5y3 * (14 + -35y)) = 0
((-28y2 + 70y3) + 5y3 * (14 + -35y)) = 0
(-28y2 + 70y3 + (14 * 5y3 + -35y * 5y3)) = 0
(-28y2 + 70y3 + (70y3 + -175y4)) = 0

Combine like terms: 70y3 + 70y3 = 140y3
(-28y2 + 140y3 + -175y4) = 0

Solving
-28y2 + 140y3 + -175y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '7y2'.
7y2(-4 + 20y + -25y2) = 0

Factor a trinomial.
7y2((-2 + 5y)(2 + -5y)) = 0

Ignore the factor 7.

Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Simplifying
y2 = 0

Take the square root of each side:
y = {0}

Subproblem 2
Set the factor '(-2 + 5y)' equal to zero and attempt to solve:

Simplifying
-2 + 5y = 0

Solving
-2 + 5y = 0

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

Add '2' to each side of the equation.
-2 + 2 + 5y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 5y = 0 + 2
5y = 0 + 2

Combine like terms: 0 + 2 = 2
5y = 2

Divide each side by '5'.
y = 0.4

Simplifying
y = 0.4

Subproblem 3
Set the factor '(2 + -5y)' equal to zero and attempt to solve:

Simplifying
2 + -5y = 0

Solving
2 + -5y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5y = 0 + -2
-5y = 0 + -2

Combine like terms: 0 + -2 = -2
-5y = -2

Divide each side by '-5'.
y = 0.4

Simplifying
y = 0.4
Solution
y = {0, 0.4, 0.4}

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