13Y^2-18Y+3=9Y^2-10Y

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Solution for 13Y^2-18Y+3=9Y^2-10Y equation: 


Simplifying
13Y2 + -18Y + 3 = 9Y2 + -10Y

Reorder the terms:
3 + -18Y + 13Y2 = 9Y2 + -10Y

Reorder the terms:
3 + -18Y + 13Y2 = -10Y + 9Y2

Solving
3 + -18Y + 13Y2 = -10Y + 9Y2

Solving for variable 'Y'.

Reorder the terms:
3 + -18Y + 10Y + 13Y2 + -9Y2 = -10Y + 9Y2 + 10Y + -9Y2

Combine like terms: -18Y + 10Y = -8Y
3 + -8Y + 13Y2 + -9Y2 = -10Y + 9Y2 + 10Y + -9Y2

Combine like terms: 13Y2 + -9Y2 = 4Y2
3 + -8Y + 4Y2 = -10Y + 9Y2 + 10Y + -9Y2

Reorder the terms:
3 + -8Y + 4Y2 = -10Y + 10Y + 9Y2 + -9Y2

Combine like terms: -10Y + 10Y = 0
3 + -8Y + 4Y2 = 0 + 9Y2 + -9Y2
3 + -8Y + 4Y2 = 9Y2 + -9Y2

Combine like terms: 9Y2 + -9Y2 = 0
3 + -8Y + 4Y2 = 0

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


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

Simplifying
1 + -2Y = 0

Solving
1 + -2Y = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2Y = 0 + -1

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

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

Divide each side by '-2'.
Y = 0.5

Simplifying
Y = 0.5

Subproblem 2
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
Solution
Y = {0.5, 1.5}

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