2y^2+5y-3=(2y-1)

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Solution for 2y^2+5y-3=(2y-1) equation: 


Simplifying
2y2 + 5y + -3 = (2y + -1)

Reorder the terms:
-3 + 5y + 2y2 = (2y + -1)

Reorder the terms:
-3 + 5y + 2y2 = (-1 + 2y)

Remove parenthesis around (-1 + 2y)
-3 + 5y + 2y2 = -1 + 2y

Solving
-3 + 5y + 2y2 = -1 + 2y

Solving for variable 'y'.

Reorder the terms:
-3 + 1 + 5y + -2y + 2y2 = -1 + 2y + 1 + -2y

Combine like terms: -3 + 1 = -2
-2 + 5y + -2y + 2y2 = -1 + 2y + 1 + -2y

Combine like terms: 5y + -2y = 3y
-2 + 3y + 2y2 = -1 + 2y + 1 + -2y

Reorder the terms:
-2 + 3y + 2y2 = -1 + 1 + 2y + -2y

Combine like terms: -1 + 1 = 0
-2 + 3y + 2y2 = 0 + 2y + -2y
-2 + 3y + 2y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
-2 + 3y + 2y2 = 0

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

Simplifying
1 + -2y = 0

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

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

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

Divide each side by '-2'.
y = 0.5

Simplifying
y = 0.5
Solution
y = {-2, 0.5}

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