4y^2+y-20=4y-13

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Solution for 4y^2+y-20=4y-13 equation: 


Simplifying
4y2 + y + -20 = 4y + -13

Reorder the terms:
-20 + y + 4y2 = 4y + -13

Reorder the terms:
-20 + y + 4y2 = -13 + 4y

Solving
-20 + y + 4y2 = -13 + 4y

Solving for variable 'y'.

Reorder the terms:
-20 + 13 + y + -4y + 4y2 = -13 + 4y + 13 + -4y

Combine like terms: -20 + 13 = -7
-7 + y + -4y + 4y2 = -13 + 4y + 13 + -4y

Combine like terms: y + -4y = -3y
-7 + -3y + 4y2 = -13 + 4y + 13 + -4y

Reorder the terms:
-7 + -3y + 4y2 = -13 + 13 + 4y + -4y

Combine like terms: -13 + 13 = 0
-7 + -3y + 4y2 = 0 + 4y + -4y
-7 + -3y + 4y2 = 4y + -4y

Combine like terms: 4y + -4y = 0
-7 + -3y + 4y2 = 0

Factor a trinomial.
(-1 + -1y)(7 + -4y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + -4y)' equal to zero and attempt to solve:

Simplifying
7 + -4y = 0

Solving
7 + -4y = 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 + -4y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4y = 0 + -7
-4y = 0 + -7

Combine like terms: 0 + -7 = -7
-4y = -7

Divide each side by '-4'.
y = 1.75

Simplifying
y = 1.75
Solution
y = {-1, 1.75}

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