(y-3)(y-3)=2y^2+2y-12

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Solution for (y-3)(y-3)=2y^2+2y-12 equation:


Simplifying
(y + -3)(y + -3) = 2y2 + 2y + -12

Reorder the terms:
(-3 + y)(y + -3) = 2y2 + 2y + -12

Reorder the terms:
(-3 + y)(-3 + y) = 2y2 + 2y + -12

Multiply (-3 + y) * (-3 + y)
(-3(-3 + y) + y(-3 + y)) = 2y2 + 2y + -12
((-3 * -3 + y * -3) + y(-3 + y)) = 2y2 + 2y + -12
((9 + -3y) + y(-3 + y)) = 2y2 + 2y + -12
(9 + -3y + (-3 * y + y * y)) = 2y2 + 2y + -12
(9 + -3y + (-3y + y2)) = 2y2 + 2y + -12

Combine like terms: -3y + -3y = -6y
(9 + -6y + y2) = 2y2 + 2y + -12

Reorder the terms:
9 + -6y + y2 = -12 + 2y + 2y2

Solving
9 + -6y + y2 = -12 + 2y + 2y2

Solving for variable 'y'.

Reorder the terms:
9 + 12 + -6y + -2y + y2 + -2y2 = -12 + 2y + 2y2 + 12 + -2y + -2y2

Combine like terms: 9 + 12 = 21
21 + -6y + -2y + y2 + -2y2 = -12 + 2y + 2y2 + 12 + -2y + -2y2

Combine like terms: -6y + -2y = -8y
21 + -8y + y2 + -2y2 = -12 + 2y + 2y2 + 12 + -2y + -2y2

Combine like terms: y2 + -2y2 = -1y2
21 + -8y + -1y2 = -12 + 2y + 2y2 + 12 + -2y + -2y2

Reorder the terms:
21 + -8y + -1y2 = -12 + 12 + 2y + -2y + 2y2 + -2y2

Combine like terms: -12 + 12 = 0
21 + -8y + -1y2 = 0 + 2y + -2y + 2y2 + -2y2
21 + -8y + -1y2 = 2y + -2y + 2y2 + -2y2

Combine like terms: 2y + -2y = 0
21 + -8y + -1y2 = 0 + 2y2 + -2y2
21 + -8y + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
21 + -8y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-21 + 8y + y2 = 0

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 8y + 21 + y2 = 0 + 21

Reorder the terms:
-21 + 21 + 8y + y2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 8y + y2 = 0 + 21
8y + y2 = 0 + 21

Combine like terms: 0 + 21 = 21
8y + y2 = 21

The y term is 8y.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8y + 16 + y2 = 21 + 16

Reorder the terms:
16 + 8y + y2 = 21 + 16

Combine like terms: 21 + 16 = 37
16 + 8y + y2 = 37

Factor a perfect square on the left side:
(y + 4)(y + 4) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(y + 4) equal to 6.08276253 and -6.08276253.

Subproblem 1

y + 4 = 6.08276253 Simplifying y + 4 = 6.08276253 Reorder the terms: 4 + y = 6.08276253 Solving 4 + y = 6.08276253 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = 6.08276253 + -4 Combine like terms: 4 + -4 = 0 0 + y = 6.08276253 + -4 y = 6.08276253 + -4 Combine like terms: 6.08276253 + -4 = 2.08276253 y = 2.08276253 Simplifying y = 2.08276253

Subproblem 2

y + 4 = -6.08276253 Simplifying y + 4 = -6.08276253 Reorder the terms: 4 + y = -6.08276253 Solving 4 + y = -6.08276253 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = -6.08276253 + -4 Combine like terms: 4 + -4 = 0 0 + y = -6.08276253 + -4 y = -6.08276253 + -4 Combine like terms: -6.08276253 + -4 = -10.08276253 y = -10.08276253 Simplifying y = -10.08276253

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.08276253, -10.08276253}

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