7y(4y-4)+21y=49

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Solution for 7y(4y-4)+21y=49 equation:


Simplifying
7y(4y + -4) + 21y = 49

Reorder the terms:
7y(-4 + 4y) + 21y = 49
(-4 * 7y + 4y * 7y) + 21y = 49
(-28y + 28y2) + 21y = 49

Reorder the terms:
-28y + 21y + 28y2 = 49

Combine like terms: -28y + 21y = -7y
-7y + 28y2 = 49

Solving
-7y + 28y2 = 49

Solving for variable 'y'.

Reorder the terms:
-49 + -7y + 28y2 = 49 + -49

Combine like terms: 49 + -49 = 0
-49 + -7y + 28y2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-7 + -1y + 4y2) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-7 + -1y + 4y2)' equal to zero and attempt to solve:

Simplifying
-7 + -1y + 4y2 = 0

Solving
-7 + -1y + 4y2 = 0

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

Divide each side by '4'.
-1.75 + -0.25y + y2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + -0.25y + 1.75 + y2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + -0.25y + y2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + -0.25y + y2 = 0 + 1.75
-0.25y + y2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
-0.25y + y2 = 1.75

The y term is -0.25y.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25y + 0.015625 + y2 = 1.75 + 0.015625

Reorder the terms:
0.015625 + -0.25y + y2 = 1.75 + 0.015625

Combine like terms: 1.75 + 0.015625 = 1.765625
0.015625 + -0.25y + y2 = 1.765625

Factor a perfect square on the left side:
(y + -0.125)(y + -0.125) = 1.765625

Calculate the square root of the right side: 1.328768227

Break this problem into two subproblems by setting 
(y + -0.125) equal to 1.328768227 and -1.328768227.


Subproblem 1
y + -0.125 = 1.328768227

Simplifying
y + -0.125 = 1.328768227

Reorder the terms:
-0.125 + y = 1.328768227

Solving
-0.125 + y = 1.328768227

Solving for variable 'y'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + y = 1.328768227 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + y = 1.328768227 + 0.125
y = 1.328768227 + 0.125

Combine like terms: 1.328768227 + 0.125 = 1.453768227
y = 1.453768227

Simplifying
y = 1.453768227


Subproblem 2
y + -0.125 = -1.328768227

Simplifying
y + -0.125 = -1.328768227

Reorder the terms:
-0.125 + y = -1.328768227

Solving
-0.125 + y = -1.328768227

Solving for variable 'y'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + y = -1.328768227 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + y = -1.328768227 + 0.125
y = -1.328768227 + 0.125

Combine like terms: -1.328768227 + 0.125 = -1.203768227
y = -1.203768227

Simplifying
y = -1.203768227


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.453768227, -1.203768227}
Solution
y = {1.453768227, -1.203768227}

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