(y^2-7)=2y^2-15y+43

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Solution for (y^2-7)=2y^2-15y+43 equation: 


Simplifying
(y2 + -7) = 2y2 + -15y + 43

Reorder the terms:
(-7 + y2) = 2y2 + -15y + 43

Remove parenthesis around (-7 + y2)
-7 + y2 = 2y2 + -15y + 43

Reorder the terms:
-7 + y2 = 43 + -15y + 2y2

Solving
-7 + y2 = 43 + -15y + 2y2

Solving for variable 'y'.

Reorder the terms:
-7 + -43 + 15y + y2 + -2y2 = 43 + -15y + 2y2 + -43 + 15y + -2y2

Combine like terms: -7 + -43 = -50
-50 + 15y + y2 + -2y2 = 43 + -15y + 2y2 + -43 + 15y + -2y2

Combine like terms: y2 + -2y2 = -1y2
-50 + 15y + -1y2 = 43 + -15y + 2y2 + -43 + 15y + -2y2

Reorder the terms:
-50 + 15y + -1y2 = 43 + -43 + -15y + 15y + 2y2 + -2y2

Combine like terms: 43 + -43 = 0
-50 + 15y + -1y2 = 0 + -15y + 15y + 2y2 + -2y2
-50 + 15y + -1y2 = -15y + 15y + 2y2 + -2y2

Combine like terms: -15y + 15y = 0
-50 + 15y + -1y2 = 0 + 2y2 + -2y2
-50 + 15y + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-50 + 15y + -1y2 = 0

Factor a trinomial.
(-10 + y)(5 + -1y) = 0


Subproblem 1
Set the factor '(-10 + y)' equal to zero and attempt to solve:

Simplifying
-10 + y = 0

Solving
-10 + y = 0

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

Add '10' to each side of the equation.
-10 + 10 + y = 0 + 10

Combine like terms: -10 + 10 = 0
0 + y = 0 + 10
y = 0 + 10

Combine like terms: 0 + 10 = 10
y = 10

Simplifying
y = 10

Subproblem 2
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 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 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Solution
y = {10, 5}

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