2y^2+5y+2=8+4y

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Solution for 2y^2+5y+2=8+4y equation: 


Simplifying
2y2 + 5y + 2 = 8 + 4y

Reorder the terms:
2 + 5y + 2y2 = 8 + 4y

Solving
2 + 5y + 2y2 = 8 + 4y

Solving for variable 'y'.

Reorder the terms:
2 + -8 + 5y + -4y + 2y2 = 8 + 4y + -8 + -4y

Combine like terms: 2 + -8 = -6
-6 + 5y + -4y + 2y2 = 8 + 4y + -8 + -4y

Combine like terms: 5y + -4y = 1y
-6 + 1y + 2y2 = 8 + 4y + -8 + -4y

Reorder the terms:
-6 + 1y + 2y2 = 8 + -8 + 4y + -4y

Combine like terms: 8 + -8 = 0
-6 + 1y + 2y2 = 0 + 4y + -4y
-6 + 1y + 2y2 = 4y + -4y

Combine like terms: 4y + -4y = 0
-6 + 1y + 2y2 = 0

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


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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 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 + -1y = 0 + 2

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

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

Divide each side by '-1'.
y = -2

Simplifying
y = -2

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 = {-2, 1.5}

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