7y(4-2y)=3(y-3)

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Solution for 7y(4-2y)=3(y-3) equation:


Simplifying
7y(4 + -2y) = 3(y + -3)
(4 * 7y + -2y * 7y) = 3(y + -3)
(28y + -14y2) = 3(y + -3)

Reorder the terms:
28y + -14y2 = 3(-3 + y)
28y + -14y2 = (-3 * 3 + y * 3)
28y + -14y2 = (-9 + 3y)

Solving
28y + -14y2 = -9 + 3y

Solving for variable 'y'.

Reorder the terms:
9 + 28y + -3y + -14y2 = -9 + 3y + 9 + -3y

Combine like terms: 28y + -3y = 25y
9 + 25y + -14y2 = -9 + 3y + 9 + -3y

Reorder the terms:
9 + 25y + -14y2 = -9 + 9 + 3y + -3y

Combine like terms: -9 + 9 = 0
9 + 25y + -14y2 = 0 + 3y + -3y
9 + 25y + -14y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
9 + 25y + -14y2 = 0

Begin completing the square.  Divide all terms by
-14 the coefficient of the squared term: 

Divide each side by '-14'.
-0.6428571429 + -1.785714286y + y2 = 0

Move the constant term to the right:

Add '0.6428571429' to each side of the equation.
-0.6428571429 + -1.785714286y + 0.6428571429 + y2 = 0 + 0.6428571429

Reorder the terms:
-0.6428571429 + 0.6428571429 + -1.785714286y + y2 = 0 + 0.6428571429

Combine like terms: -0.6428571429 + 0.6428571429 = 0.0000000000
0.0000000000 + -1.785714286y + y2 = 0 + 0.6428571429
-1.785714286y + y2 = 0 + 0.6428571429

Combine like terms: 0 + 0.6428571429 = 0.6428571429
-1.785714286y + y2 = 0.6428571429

The y term is -1.785714286y.  Take half its coefficient (-0.892857143).
Square it (0.7971938778) and add it to both sides.

Add '0.7971938778' to each side of the equation.
-1.785714286y + 0.7971938778 + y2 = 0.6428571429 + 0.7971938778

Reorder the terms:
0.7971938778 + -1.785714286y + y2 = 0.6428571429 + 0.7971938778

Combine like terms: 0.6428571429 + 0.7971938778 = 1.4400510207
0.7971938778 + -1.785714286y + y2 = 1.4400510207

Factor a perfect square on the left side:
(y + -0.892857143)(y + -0.892857143) = 1.4400510207

Calculate the square root of the right side: 1.200021258

Break this problem into two subproblems by setting 
(y + -0.892857143) equal to 1.200021258 and -1.200021258.

Subproblem 1

y + -0.892857143 = 1.200021258 Simplifying y + -0.892857143 = 1.200021258 Reorder the terms: -0.892857143 + y = 1.200021258 Solving -0.892857143 + y = 1.200021258 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.892857143' to each side of the equation. -0.892857143 + 0.892857143 + y = 1.200021258 + 0.892857143 Combine like terms: -0.892857143 + 0.892857143 = 0.000000000 0.000000000 + y = 1.200021258 + 0.892857143 y = 1.200021258 + 0.892857143 Combine like terms: 1.200021258 + 0.892857143 = 2.092878401 y = 2.092878401 Simplifying y = 2.092878401

Subproblem 2

y + -0.892857143 = -1.200021258 Simplifying y + -0.892857143 = -1.200021258 Reorder the terms: -0.892857143 + y = -1.200021258 Solving -0.892857143 + y = -1.200021258 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.892857143' to each side of the equation. -0.892857143 + 0.892857143 + y = -1.200021258 + 0.892857143 Combine like terms: -0.892857143 + 0.892857143 = 0.000000000 0.000000000 + y = -1.200021258 + 0.892857143 y = -1.200021258 + 0.892857143 Combine like terms: -1.200021258 + 0.892857143 = -0.307164115 y = -0.307164115 Simplifying y = -0.307164115

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.092878401, -0.307164115}

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