2y^2+4y-1=7y^2-7y+1

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Solution for 2y^2+4y-1=7y^2-7y+1 equation: 


Simplifying
2y2 + 4y + -1 = 7y2 + -7y + 1

Reorder the terms:
-1 + 4y + 2y2 = 7y2 + -7y + 1

Reorder the terms:
-1 + 4y + 2y2 = 1 + -7y + 7y2

Solving
-1 + 4y + 2y2 = 1 + -7y + 7y2

Solving for variable 'y'.

Reorder the terms:
-1 + -1 + 4y + 7y + 2y2 + -7y2 = 1 + -7y + 7y2 + -1 + 7y + -7y2

Combine like terms: -1 + -1 = -2
-2 + 4y + 7y + 2y2 + -7y2 = 1 + -7y + 7y2 + -1 + 7y + -7y2

Combine like terms: 4y + 7y = 11y
-2 + 11y + 2y2 + -7y2 = 1 + -7y + 7y2 + -1 + 7y + -7y2

Combine like terms: 2y2 + -7y2 = -5y2
-2 + 11y + -5y2 = 1 + -7y + 7y2 + -1 + 7y + -7y2

Reorder the terms:
-2 + 11y + -5y2 = 1 + -1 + -7y + 7y + 7y2 + -7y2

Combine like terms: 1 + -1 = 0
-2 + 11y + -5y2 = 0 + -7y + 7y + 7y2 + -7y2
-2 + 11y + -5y2 = -7y + 7y + 7y2 + -7y2

Combine like terms: -7y + 7y = 0
-2 + 11y + -5y2 = 0 + 7y2 + -7y2
-2 + 11y + -5y2 = 7y2 + -7y2

Combine like terms: 7y2 + -7y2 = 0
-2 + 11y + -5y2 = 0

Factor a trinomial.
(-2 + y)(1 + -5y) = 0


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

Simplifying
-2 + y = 0

Solving
-2 + y = 0

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

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

Combine like terms: -2 + 2 = 0
0 + y = 0 + 2
y = 0 + 2

Combine like terms: 0 + 2 = 2
y = 2

Simplifying
y = 2

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

Simplifying
1 + -5y = 0

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

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

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

Divide each side by '-5'.
y = 0.2

Simplifying
y = 0.2
Solution
y = {2, 0.2}

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