5y^2-17y+10=2y^2-14

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Solution for 5y^2-17y+10=2y^2-14 equation: 


Simplifying
5y2 + -17y + 10 = 2y2 + -14

Reorder the terms:
10 + -17y + 5y2 = 2y2 + -14

Reorder the terms:
10 + -17y + 5y2 = -14 + 2y2

Solving
10 + -17y + 5y2 = -14 + 2y2

Solving for variable 'y'.

Reorder the terms:
10 + 14 + -17y + 5y2 + -2y2 = -14 + 2y2 + 14 + -2y2

Combine like terms: 10 + 14 = 24
24 + -17y + 5y2 + -2y2 = -14 + 2y2 + 14 + -2y2

Combine like terms: 5y2 + -2y2 = 3y2
24 + -17y + 3y2 = -14 + 2y2 + 14 + -2y2

Reorder the terms:
24 + -17y + 3y2 = -14 + 14 + 2y2 + -2y2

Combine like terms: -14 + 14 = 0
24 + -17y + 3y2 = 0 + 2y2 + -2y2
24 + -17y + 3y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
24 + -17y + 3y2 = 0

Factor a trinomial.
(8 + -3y)(3 + -1y) = 0


Subproblem 1
Set the factor '(8 + -3y)' equal to zero and attempt to solve:

Simplifying
8 + -3y = 0

Solving
8 + -3y = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3y = 0 + -8
-3y = 0 + -8

Combine like terms: 0 + -8 = -8
-3y = -8

Divide each side by '-3'.
y = 2.666666667

Simplifying
y = 2.666666667

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

Simplifying
3 + -1y = 0

Solving
3 + -1y = 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 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {2.666666667, 3}

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