3+y=12-4y(y+1)

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Solution for 3+y=12-4y(y+1) equation: 


Simplifying
3 + y = 12 + -4y(y + 1)

Reorder the terms:
3 + y = 12 + -4y(1 + y)
3 + y = 12 + (1 * -4y + y * -4y)
3 + y = 12 + (-4y + -4y2)

Solving
3 + y = 12 + -4y + -4y2

Solving for variable 'y'.

Reorder the terms:
3 + -12 + y + 4y + 4y2 = 12 + -4y + -4y2 + -12 + 4y + 4y2

Combine like terms: 3 + -12 = -9
-9 + y + 4y + 4y2 = 12 + -4y + -4y2 + -12 + 4y + 4y2

Combine like terms: y + 4y = 5y
-9 + 5y + 4y2 = 12 + -4y + -4y2 + -12 + 4y + 4y2

Reorder the terms:
-9 + 5y + 4y2 = 12 + -12 + -4y + 4y + -4y2 + 4y2

Combine like terms: 12 + -12 = 0
-9 + 5y + 4y2 = 0 + -4y + 4y + -4y2 + 4y2
-9 + 5y + 4y2 = -4y + 4y + -4y2 + 4y2

Combine like terms: -4y + 4y = 0
-9 + 5y + 4y2 = 0 + -4y2 + 4y2
-9 + 5y + 4y2 = -4y2 + 4y2

Combine like terms: -4y2 + 4y2 = 0
-9 + 5y + 4y2 = 0

Factor a trinomial.
(-9 + -4y)(1 + -1y) = 0


Subproblem 1
Set the factor '(-9 + -4y)' equal to zero and attempt to solve:

Simplifying
-9 + -4y = 0

Solving
-9 + -4y = 0

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

Add '9' to each side of the equation.
-9 + 9 + -4y = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -4y = 0 + 9
-4y = 0 + 9

Combine like terms: 0 + 9 = 9
-4y = 9

Divide each side by '-4'.
y = -2.25

Simplifying
y = -2.25

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 = {-2.25, 1}

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