4(y+4)y=3(y+2)-4

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Solution for 4(y+4)y=3(y+2)-4 equation:


Simplifying
4(y + 4) * y = 3(y + 2) + -4

Reorder the terms:
4(4 + y) * y = 3(y + 2) + -4

Reorder the terms for easier multiplication:
4y(4 + y) = 3(y + 2) + -4
(4 * 4y + y * 4y) = 3(y + 2) + -4
(16y + 4y2) = 3(y + 2) + -4

Reorder the terms:
16y + 4y2 = 3(2 + y) + -4
16y + 4y2 = (2 * 3 + y * 3) + -4
16y + 4y2 = (6 + 3y) + -4

Reorder the terms:
16y + 4y2 = 6 + -4 + 3y

Combine like terms: 6 + -4 = 2
16y + 4y2 = 2 + 3y

Solving
16y + 4y2 = 2 + 3y

Solving for variable 'y'.

Reorder the terms:
-2 + 16y + -3y + 4y2 = 2 + 3y + -2 + -3y

Combine like terms: 16y + -3y = 13y
-2 + 13y + 4y2 = 2 + 3y + -2 + -3y

Reorder the terms:
-2 + 13y + 4y2 = 2 + -2 + 3y + -3y

Combine like terms: 2 + -2 = 0
-2 + 13y + 4y2 = 0 + 3y + -3y
-2 + 13y + 4y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
-2 + 13y + 4y2 = 0

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

Divide each side by '4'.
-0.5 + 3.25y + y2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 3.25y + 0.5 + y2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 3.25y + y2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 3.25y + y2 = 0 + 0.5
3.25y + y2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
3.25y + y2 = 0.5

The y term is 3.25y.  Take half its coefficient (1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
3.25y + 2.640625 + y2 = 0.5 + 2.640625

Reorder the terms:
2.640625 + 3.25y + y2 = 0.5 + 2.640625

Combine like terms: 0.5 + 2.640625 = 3.140625
2.640625 + 3.25y + y2 = 3.140625

Factor a perfect square on the left side:
(y + 1.625)(y + 1.625) = 3.140625

Calculate the square root of the right side: 1.77218086

Break this problem into two subproblems by setting 
(y + 1.625) equal to 1.77218086 and -1.77218086.

Subproblem 1

y + 1.625 = 1.77218086 Simplifying y + 1.625 = 1.77218086 Reorder the terms: 1.625 + y = 1.77218086 Solving 1.625 + y = 1.77218086 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + y = 1.77218086 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + y = 1.77218086 + -1.625 y = 1.77218086 + -1.625 Combine like terms: 1.77218086 + -1.625 = 0.14718086 y = 0.14718086 Simplifying y = 0.14718086

Subproblem 2

y + 1.625 = -1.77218086 Simplifying y + 1.625 = -1.77218086 Reorder the terms: 1.625 + y = -1.77218086 Solving 1.625 + y = -1.77218086 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + y = -1.77218086 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + y = -1.77218086 + -1.625 y = -1.77218086 + -1.625 Combine like terms: -1.77218086 + -1.625 = -3.39718086 y = -3.39718086 Simplifying y = -3.39718086

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.14718086, -3.39718086}

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