25-y^2=100-40y-4y^2

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Solution for 25-y^2=100-40y-4y^2 equation: 


Simplifying
25 + -1y2 = 100 + -40y + -4y2

Solving
25 + -1y2 = 100 + -40y + -4y2

Solving for variable 'y'.

Reorder the terms:
25 + -100 + 40y + -1y2 + 4y2 = 100 + -40y + -4y2 + -100 + 40y + 4y2

Combine like terms: 25 + -100 = -75
-75 + 40y + -1y2 + 4y2 = 100 + -40y + -4y2 + -100 + 40y + 4y2

Combine like terms: -1y2 + 4y2 = 3y2
-75 + 40y + 3y2 = 100 + -40y + -4y2 + -100 + 40y + 4y2

Reorder the terms:
-75 + 40y + 3y2 = 100 + -100 + -40y + 40y + -4y2 + 4y2

Combine like terms: 100 + -100 = 0
-75 + 40y + 3y2 = 0 + -40y + 40y + -4y2 + 4y2
-75 + 40y + 3y2 = -40y + 40y + -4y2 + 4y2

Combine like terms: -40y + 40y = 0
-75 + 40y + 3y2 = 0 + -4y2 + 4y2
-75 + 40y + 3y2 = -4y2 + 4y2

Combine like terms: -4y2 + 4y2 = 0
-75 + 40y + 3y2 = 0

Factor a trinomial.
(-15 + -1y)(5 + -3y) = 0


Subproblem 1
Set the factor '(-15 + -1y)' equal to zero and attempt to solve:

Simplifying
-15 + -1y = 0

Solving
-15 + -1y = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1y = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1y = 0 + 15
-1y = 0 + 15

Combine like terms: 0 + 15 = 15
-1y = 15

Divide each side by '-1'.
y = -15

Simplifying
y = -15

Subproblem 2
Set the factor '(5 + -3y)' equal to zero and attempt to solve:

Simplifying
5 + -3y = 0

Solving
5 + -3y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3y = 0 + -5
-3y = 0 + -5

Combine like terms: 0 + -5 = -5
-3y = -5

Divide each side by '-3'.
y = 1.666666667

Simplifying
y = 1.666666667
Solution
y = {-15, 1.666666667}

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