5y(3y-1)=-6y+2

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Solution for 5y(3y-1)=-6y+2 equation: 


Simplifying
5y(3y + -1) = -6y + 2

Reorder the terms:
5y(-1 + 3y) = -6y + 2
(-1 * 5y + 3y * 5y) = -6y + 2
(-5y + 15y2) = -6y + 2

Reorder the terms:
-5y + 15y2 = 2 + -6y

Solving
-5y + 15y2 = 2 + -6y

Solving for variable 'y'.

Reorder the terms:
-2 + -5y + 6y + 15y2 = 2 + -6y + -2 + 6y

Combine like terms: -5y + 6y = 1y
-2 + 1y + 15y2 = 2 + -6y + -2 + 6y

Reorder the terms:
-2 + 1y + 15y2 = 2 + -2 + -6y + 6y

Combine like terms: 2 + -2 = 0
-2 + 1y + 15y2 = 0 + -6y + 6y
-2 + 1y + 15y2 = -6y + 6y

Combine like terms: -6y + 6y = 0
-2 + 1y + 15y2 = 0

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


Subproblem 1
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 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 = {-0.4, 0.3333333333}

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