y(y-6)=(5y^2-36)-(4y^2-3y)

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Solution for y(y-6)=(5y^2-36)-(4y^2-3y) equation: 


Simplifying
y(y + -6) = (5y2 + -36) + -1(4y2 + -3y)

Reorder the terms:
y(-6 + y) = (5y2 + -36) + -1(4y2 + -3y)
(-6 * y + y * y) = (5y2 + -36) + -1(4y2 + -3y)
(-6y + y2) = (5y2 + -36) + -1(4y2 + -3y)

Reorder the terms:
-6y + y2 = (-36 + 5y2) + -1(4y2 + -3y)

Remove parenthesis around (-36 + 5y2)
-6y + y2 = -36 + 5y2 + -1(4y2 + -3y)

Reorder the terms:
-6y + y2 = -36 + 5y2 + -1(-3y + 4y2)
-6y + y2 = -36 + 5y2 + (-3y * -1 + 4y2 * -1)
-6y + y2 = -36 + 5y2 + (3y + -4y2)

Reorder the terms:
-6y + y2 = -36 + 3y + 5y2 + -4y2

Combine like terms: 5y2 + -4y2 = 1y2
-6y + y2 = -36 + 3y + 1y2

Solving
-6y + y2 = -36 + 3y + 1y2

Solving for variable 'y'.

Reorder the terms:
36 + -6y + -3y + y2 + -1y2 = -36 + 3y + 1y2 + 36 + -3y + -1y2

Combine like terms: -6y + -3y = -9y
36 + -9y + y2 + -1y2 = -36 + 3y + 1y2 + 36 + -3y + -1y2

Combine like terms: y2 + -1y2 = 0
36 + -9y + 0 = -36 + 3y + 1y2 + 36 + -3y + -1y2
36 + -9y = -36 + 3y + 1y2 + 36 + -3y + -1y2

Reorder the terms:
36 + -9y = -36 + 36 + 3y + -3y + 1y2 + -1y2

Combine like terms: -36 + 36 = 0
36 + -9y = 0 + 3y + -3y + 1y2 + -1y2
36 + -9y = 3y + -3y + 1y2 + -1y2

Combine like terms: 3y + -3y = 0
36 + -9y = 0 + 1y2 + -1y2
36 + -9y = 1y2 + -1y2

Combine like terms: 1y2 + -1y2 = 0
36 + -9y = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(4 + -1y) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {4}

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