(y+2)(y+2)=2y^2-7y+32

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Solution for (y+2)(y+2)=2y^2-7y+32 equation: 


Simplifying
(y + 2)(y + 2) = 2y2 + -7y + 32

Reorder the terms:
(2 + y)(y + 2) = 2y2 + -7y + 32

Reorder the terms:
(2 + y)(2 + y) = 2y2 + -7y + 32

Multiply (2 + y) * (2 + y)
(2(2 + y) + y(2 + y)) = 2y2 + -7y + 32
((2 * 2 + y * 2) + y(2 + y)) = 2y2 + -7y + 32
((4 + 2y) + y(2 + y)) = 2y2 + -7y + 32
(4 + 2y + (2 * y + y * y)) = 2y2 + -7y + 32
(4 + 2y + (2y + y2)) = 2y2 + -7y + 32

Combine like terms: 2y + 2y = 4y
(4 + 4y + y2) = 2y2 + -7y + 32

Reorder the terms:
4 + 4y + y2 = 32 + -7y + 2y2

Solving
4 + 4y + y2 = 32 + -7y + 2y2

Solving for variable 'y'.

Reorder the terms:
4 + -32 + 4y + 7y + y2 + -2y2 = 32 + -7y + 2y2 + -32 + 7y + -2y2

Combine like terms: 4 + -32 = -28
-28 + 4y + 7y + y2 + -2y2 = 32 + -7y + 2y2 + -32 + 7y + -2y2

Combine like terms: 4y + 7y = 11y
-28 + 11y + y2 + -2y2 = 32 + -7y + 2y2 + -32 + 7y + -2y2

Combine like terms: y2 + -2y2 = -1y2
-28 + 11y + -1y2 = 32 + -7y + 2y2 + -32 + 7y + -2y2

Reorder the terms:
-28 + 11y + -1y2 = 32 + -32 + -7y + 7y + 2y2 + -2y2

Combine like terms: 32 + -32 = 0
-28 + 11y + -1y2 = 0 + -7y + 7y + 2y2 + -2y2
-28 + 11y + -1y2 = -7y + 7y + 2y2 + -2y2

Combine like terms: -7y + 7y = 0
-28 + 11y + -1y2 = 0 + 2y2 + -2y2
-28 + 11y + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-28 + 11y + -1y2 = 0

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


Subproblem 1
Set the factor '(-7 + y)' equal to zero and attempt to solve:

Simplifying
-7 + y = 0

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

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

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

Simplifying
y = 7

Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {7, 4}

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