(y-2)(y-9)=9y+6

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Solution for (y-2)(y-9)=9y+6 equation:


Simplifying
(y + -2)(y + -9) = 9y + 6

Reorder the terms:
(-2 + y)(y + -9) = 9y + 6

Reorder the terms:
(-2 + y)(-9 + y) = 9y + 6

Multiply (-2 + y) * (-9 + y)
(-2(-9 + y) + y(-9 + y)) = 9y + 6
((-9 * -2 + y * -2) + y(-9 + y)) = 9y + 6
((18 + -2y) + y(-9 + y)) = 9y + 6
(18 + -2y + (-9 * y + y * y)) = 9y + 6
(18 + -2y + (-9y + y2)) = 9y + 6

Combine like terms: -2y + -9y = -11y
(18 + -11y + y2) = 9y + 6

Reorder the terms:
18 + -11y + y2 = 6 + 9y

Solving
18 + -11y + y2 = 6 + 9y

Solving for variable 'y'.

Reorder the terms:
18 + -6 + -11y + -9y + y2 = 6 + 9y + -6 + -9y

Combine like terms: 18 + -6 = 12
12 + -11y + -9y + y2 = 6 + 9y + -6 + -9y

Combine like terms: -11y + -9y = -20y
12 + -20y + y2 = 6 + 9y + -6 + -9y

Reorder the terms:
12 + -20y + y2 = 6 + -6 + 9y + -9y

Combine like terms: 6 + -6 = 0
12 + -20y + y2 = 0 + 9y + -9y
12 + -20y + y2 = 9y + -9y

Combine like terms: 9y + -9y = 0
12 + -20y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -20y + -12 + y2 = 0 + -12

Reorder the terms:
12 + -12 + -20y + y2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -20y + y2 = 0 + -12
-20y + y2 = 0 + -12

Combine like terms: 0 + -12 = -12
-20y + y2 = -12

The y term is -20y.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20y + 100 + y2 = -12 + 100

Reorder the terms:
100 + -20y + y2 = -12 + 100

Combine like terms: -12 + 100 = 88
100 + -20y + y2 = 88

Factor a perfect square on the left side:
(y + -10)(y + -10) = 88

Calculate the square root of the right side: 9.38083152

Break this problem into two subproblems by setting 
(y + -10) equal to 9.38083152 and -9.38083152.

Subproblem 1

y + -10 = 9.38083152 Simplifying y + -10 = 9.38083152 Reorder the terms: -10 + y = 9.38083152 Solving -10 + y = 9.38083152 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + y = 9.38083152 + 10 Combine like terms: -10 + 10 = 0 0 + y = 9.38083152 + 10 y = 9.38083152 + 10 Combine like terms: 9.38083152 + 10 = 19.38083152 y = 19.38083152 Simplifying y = 19.38083152

Subproblem 2

y + -10 = -9.38083152 Simplifying y + -10 = -9.38083152 Reorder the terms: -10 + y = -9.38083152 Solving -10 + y = -9.38083152 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + y = -9.38083152 + 10 Combine like terms: -10 + 10 = 0 0 + y = -9.38083152 + 10 y = -9.38083152 + 10 Combine like terms: -9.38083152 + 10 = 0.61916848 y = 0.61916848 Simplifying y = 0.61916848

Solution

The solution to the problem is based on the solutions from the subproblems. y = {19.38083152, 0.61916848}

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