2y^2-7y+6=y^2-10y+24

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Solution for 2y^2-7y+6=y^2-10y+24 equation: 


Simplifying
2y2 + -7y + 6 = y2 + -10y + 24

Reorder the terms:
6 + -7y + 2y2 = y2 + -10y + 24

Reorder the terms:
6 + -7y + 2y2 = 24 + -10y + y2

Solving
6 + -7y + 2y2 = 24 + -10y + y2

Solving for variable 'y'.

Reorder the terms:
6 + -24 + -7y + 10y + 2y2 + -1y2 = 24 + -10y + y2 + -24 + 10y + -1y2

Combine like terms: 6 + -24 = -18
-18 + -7y + 10y + 2y2 + -1y2 = 24 + -10y + y2 + -24 + 10y + -1y2

Combine like terms: -7y + 10y = 3y
-18 + 3y + 2y2 + -1y2 = 24 + -10y + y2 + -24 + 10y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-18 + 3y + 1y2 = 24 + -10y + y2 + -24 + 10y + -1y2

Reorder the terms:
-18 + 3y + 1y2 = 24 + -24 + -10y + 10y + y2 + -1y2

Combine like terms: 24 + -24 = 0
-18 + 3y + 1y2 = 0 + -10y + 10y + y2 + -1y2
-18 + 3y + 1y2 = -10y + 10y + y2 + -1y2

Combine like terms: -10y + 10y = 0
-18 + 3y + 1y2 = 0 + y2 + -1y2
-18 + 3y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-18 + 3y + 1y2 = 0

Factor a trinomial.
(-6 + -1y)(3 + -1y) = 0


Subproblem 1
Set the factor '(-6 + -1y)' equal to zero and attempt to solve:

Simplifying
-6 + -1y = 0

Solving
-6 + -1y = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1y = 0 + 6
-1y = 0 + 6

Combine like terms: 0 + 6 = 6
-1y = 6

Divide each side by '-1'.
y = -6

Simplifying
y = -6

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 = {-6, 3}

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