5y(y-3)=3y-15

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Solution for 5y(y-3)=3y-15 equation:


Simplifying
5y(y + -3) = 3y + -15

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

Reorder the terms:
-15y + 5y2 = -15 + 3y

Solving
-15y + 5y2 = -15 + 3y

Solving for variable 'y'.

Reorder the terms:
15 + -15y + -3y + 5y2 = -15 + 3y + 15 + -3y

Combine like terms: -15y + -3y = -18y
15 + -18y + 5y2 = -15 + 3y + 15 + -3y

Reorder the terms:
15 + -18y + 5y2 = -15 + 15 + 3y + -3y

Combine like terms: -15 + 15 = 0
15 + -18y + 5y2 = 0 + 3y + -3y
15 + -18y + 5y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
15 + -18y + 5y2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
3 + -3.6y + y2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -3.6y + -3 + y2 = 0 + -3

Reorder the terms:
3 + -3 + -3.6y + y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -3.6y + y2 = 0 + -3
-3.6y + y2 = 0 + -3

Combine like terms: 0 + -3 = -3
-3.6y + y2 = -3

The y term is -3.6y.  Take half its coefficient (-1.8).
Square it (3.24) and add it to both sides.

Add '3.24' to each side of the equation.
-3.6y + 3.24 + y2 = -3 + 3.24

Reorder the terms:
3.24 + -3.6y + y2 = -3 + 3.24

Combine like terms: -3 + 3.24 = 0.24
3.24 + -3.6y + y2 = 0.24

Factor a perfect square on the left side:
(y + -1.8)(y + -1.8) = 0.24

Calculate the square root of the right side: 0.489897949

Break this problem into two subproblems by setting 
(y + -1.8) equal to 0.489897949 and -0.489897949.

Subproblem 1

y + -1.8 = 0.489897949 Simplifying y + -1.8 = 0.489897949 Reorder the terms: -1.8 + y = 0.489897949 Solving -1.8 + y = 0.489897949 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + y = 0.489897949 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + y = 0.489897949 + 1.8 y = 0.489897949 + 1.8 Combine like terms: 0.489897949 + 1.8 = 2.289897949 y = 2.289897949 Simplifying y = 2.289897949

Subproblem 2

y + -1.8 = -0.489897949 Simplifying y + -1.8 = -0.489897949 Reorder the terms: -1.8 + y = -0.489897949 Solving -1.8 + y = -0.489897949 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + y = -0.489897949 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + y = -0.489897949 + 1.8 y = -0.489897949 + 1.8 Combine like terms: -0.489897949 + 1.8 = 1.310102051 y = 1.310102051 Simplifying y = 1.310102051

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.289897949, 1.310102051}

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