6y^2+24y+9=5y^2+33y-5

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Solution for 6y^2+24y+9=5y^2+33y-5 equation:


Simplifying
6y2 + 24y + 9 = 5y2 + 33y + -5

Reorder the terms:
9 + 24y + 6y2 = 5y2 + 33y + -5

Reorder the terms:
9 + 24y + 6y2 = -5 + 33y + 5y2

Solving
9 + 24y + 6y2 = -5 + 33y + 5y2

Solving for variable 'y'.

Reorder the terms:
9 + 5 + 24y + -33y + 6y2 + -5y2 = -5 + 33y + 5y2 + 5 + -33y + -5y2

Combine like terms: 9 + 5 = 14
14 + 24y + -33y + 6y2 + -5y2 = -5 + 33y + 5y2 + 5 + -33y + -5y2

Combine like terms: 24y + -33y = -9y
14 + -9y + 6y2 + -5y2 = -5 + 33y + 5y2 + 5 + -33y + -5y2

Combine like terms: 6y2 + -5y2 = 1y2
14 + -9y + 1y2 = -5 + 33y + 5y2 + 5 + -33y + -5y2

Reorder the terms:
14 + -9y + 1y2 = -5 + 5 + 33y + -33y + 5y2 + -5y2

Combine like terms: -5 + 5 = 0
14 + -9y + 1y2 = 0 + 33y + -33y + 5y2 + -5y2
14 + -9y + 1y2 = 33y + -33y + 5y2 + -5y2

Combine like terms: 33y + -33y = 0
14 + -9y + 1y2 = 0 + 5y2 + -5y2
14 + -9y + 1y2 = 5y2 + -5y2

Combine like terms: 5y2 + -5y2 = 0
14 + -9y + 1y2 = 0

Factor a trinomial.
(2 + -1y)(7 + -1y) = 0


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

Simplifying
2 + -1y = 0

Solving
2 + -1y = 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 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2

Subproblem 2
Set the factor '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

Simplifying
y = 7
Solution
y = {2, 7}

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