3(y^2-6)=y(y+7)-3

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Solution for 3(y^2-6)=y(y+7)-3 equation: 


Simplifying
3(y2 + -6) = y(y + 7) + -3

Reorder the terms:
3(-6 + y2) = y(y + 7) + -3
(-6 * 3 + y2 * 3) = y(y + 7) + -3
(-18 + 3y2) = y(y + 7) + -3

Reorder the terms:
-18 + 3y2 = y(7 + y) + -3
-18 + 3y2 = (7 * y + y * y) + -3
-18 + 3y2 = (7y + y2) + -3

Reorder the terms:
-18 + 3y2 = -3 + 7y + y2

Solving
-18 + 3y2 = -3 + 7y + y2

Solving for variable 'y'.

Reorder the terms:
-18 + 3 + -7y + 3y2 + -1y2 = -3 + 7y + y2 + 3 + -7y + -1y2

Combine like terms: -18 + 3 = -15
-15 + -7y + 3y2 + -1y2 = -3 + 7y + y2 + 3 + -7y + -1y2

Combine like terms: 3y2 + -1y2 = 2y2
-15 + -7y + 2y2 = -3 + 7y + y2 + 3 + -7y + -1y2

Reorder the terms:
-15 + -7y + 2y2 = -3 + 3 + 7y + -7y + y2 + -1y2

Combine like terms: -3 + 3 = 0
-15 + -7y + 2y2 = 0 + 7y + -7y + y2 + -1y2
-15 + -7y + 2y2 = 7y + -7y + y2 + -1y2

Combine like terms: 7y + -7y = 0
-15 + -7y + 2y2 = 0 + y2 + -1y2
-15 + -7y + 2y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-15 + -7y + 2y2 = 0

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


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

Simplifying
-3 + -2y = 0

Solving
-3 + -2y = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2y = 0 + 3
-2y = 0 + 3

Combine like terms: 0 + 3 = 3
-2y = 3

Divide each side by '-2'.
y = -1.5

Simplifying
y = -1.5

Subproblem 2
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
Solution
y = {-1.5, 5}

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