3y(10-2y)=2y-10

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Solution for 3y(10-2y)=2y-10 equation: 


Simplifying
3y(10 + -2y) = 2y + -10
(10 * 3y + -2y * 3y) = 2y + -10
(30y + -6y2) = 2y + -10

Reorder the terms:
30y + -6y2 = -10 + 2y

Solving
30y + -6y2 = -10 + 2y

Solving for variable 'y'.

Reorder the terms:
10 + 30y + -2y + -6y2 = -10 + 2y + 10 + -2y

Combine like terms: 30y + -2y = 28y
10 + 28y + -6y2 = -10 + 2y + 10 + -2y

Reorder the terms:
10 + 28y + -6y2 = -10 + 10 + 2y + -2y

Combine like terms: -10 + 10 = 0
10 + 28y + -6y2 = 0 + 2y + -2y
10 + 28y + -6y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
10 + 28y + -6y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 14y + -3y2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5

Subproblem 2
Set the factor '(1 + 3y)' equal to zero and attempt to solve:

Simplifying
1 + 3y = 0

Solving
1 + 3y = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3y = 0 + -1
3y = 0 + -1

Combine like terms: 0 + -1 = -1
3y = -1

Divide each side by '3'.
y = -0.3333333333

Simplifying
y = -0.3333333333
Solution
y = {5, -0.3333333333}

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