2y^2+20y=8y+14

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Solution for 2y^2+20y=8y+14 equation: 


Simplifying
2y2 + 20y = 8y + 14

Reorder the terms:
20y + 2y2 = 8y + 14

Reorder the terms:
20y + 2y2 = 14 + 8y

Solving
20y + 2y2 = 14 + 8y

Solving for variable 'y'.

Reorder the terms:
-14 + 20y + -8y + 2y2 = 14 + 8y + -14 + -8y

Combine like terms: 20y + -8y = 12y
-14 + 12y + 2y2 = 14 + 8y + -14 + -8y

Reorder the terms:
-14 + 12y + 2y2 = 14 + -14 + 8y + -8y

Combine like terms: 14 + -14 = 0
-14 + 12y + 2y2 = 0 + 8y + -8y
-14 + 12y + 2y2 = 8y + -8y

Combine like terms: 8y + -8y = 0
-14 + 12y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 6y + y2) = 0

Factor a trinomial.
2((-7 + -1y)(1 + -1y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -1y)' equal to zero and attempt to solve:

Simplifying
-7 + -1y = 0

Solving
-7 + -1y = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1y = 0 + 7
-1y = 0 + 7

Combine like terms: 0 + 7 = 7
-1y = 7

Divide each side by '-1'.
y = -7

Simplifying
y = -7

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

Simplifying
1 + -1y = 0

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

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

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

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

Simplifying
y = 1
Solution
y = {-7, 1}

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