(2y+4)(2y+4)+y^2=4

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Solution for (2y+4)(2y+4)+y^2=4 equation: 


Simplifying
(2y + 4)(2y + 4) + y2 = 4

Reorder the terms:
(4 + 2y)(2y + 4) + y2 = 4

Reorder the terms:
(4 + 2y)(4 + 2y) + y2 = 4

Multiply (4 + 2y) * (4 + 2y)
(4(4 + 2y) + 2y * (4 + 2y)) + y2 = 4
((4 * 4 + 2y * 4) + 2y * (4 + 2y)) + y2 = 4
((16 + 8y) + 2y * (4 + 2y)) + y2 = 4
(16 + 8y + (4 * 2y + 2y * 2y)) + y2 = 4
(16 + 8y + (8y + 4y2)) + y2 = 4

Combine like terms: 8y + 8y = 16y
(16 + 16y + 4y2) + y2 = 4

Combine like terms: 4y2 + y2 = 5y2
16 + 16y + 5y2 = 4

Solving
16 + 16y + 5y2 = 4

Solving for variable 'y'.

Reorder the terms:
16 + -4 + 16y + 5y2 = 4 + -4

Combine like terms: 16 + -4 = 12
12 + 16y + 5y2 = 4 + -4

Combine like terms: 4 + -4 = 0
12 + 16y + 5y2 = 0

Factor a trinomial.
(2 + y)(6 + 5y) = 0


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

Simplifying
2 + y = 0

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

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

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

Simplifying
y = -2

Subproblem 2
Set the factor '(6 + 5y)' equal to zero and attempt to solve:

Simplifying
6 + 5y = 0

Solving
6 + 5y = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5y = 0 + -6
5y = 0 + -6

Combine like terms: 0 + -6 = -6
5y = -6

Divide each side by '5'.
y = -1.2

Simplifying
y = -1.2
Solution
y = {-2, -1.2}

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