5y^2+3y=14

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Solution for 5y^2+3y=14 equation: 


Simplifying
5y2 + 3y = 14

Reorder the terms:
3y + 5y2 = 14

Solving
3y + 5y2 = 14

Solving for variable 'y'.

Reorder the terms:
-14 + 3y + 5y2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + 3y + 5y2 = 0

Factor a trinomial.
(-2 + -1y)(7 + -5y) = 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 '(7 + -5y)' equal to zero and attempt to solve:

Simplifying
7 + -5y = 0

Solving
7 + -5y = 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 + -5y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5y = 0 + -7
-5y = 0 + -7

Combine like terms: 0 + -7 = -7
-5y = -7

Divide each side by '-5'.
y = 1.4

Simplifying
y = 1.4
Solution
y = {-2, 1.4}

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