-3=12y(2y-7)

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Solution for -3=12y(2y-7) equation: 


Simplifying
-3 = 12y(2y + -7)

Reorder the terms:
-3 = 12y(-7 + 2y)
-3 = (-7 * 12y + 2y * 12y)
-3 = (-84y + 24y2)

Solving
-3 = -84y + 24y2

Solving for variable 'y'.

Reorder the terms:
-3 + 84y + -24y2 = -84y + 84y + 24y2 + -24y2

Combine like terms: -84y + 84y = 0
-3 + 84y + -24y2 = 0 + 24y2 + -24y2
-3 + 84y + -24y2 = 24y2 + -24y2

Combine like terms: 24y2 + -24y2 = 0
-3 + 84y + -24y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 28y + -8y2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-1 + 28y + -8y2)' equal to zero and attempt to solve:

Simplifying
-1 + 28y + -8y2 = 0

Solving
-1 + 28y + -8y2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
0.125 + -3.5y + y2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -3.5y + -0.125 + y2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -3.5y + y2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -3.5y + y2 = 0 + -0.125
-3.5y + y2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-3.5y + y2 = -0.125

The y term is -3.5y.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5y + 3.0625 + y2 = -0.125 + 3.0625

Reorder the terms:
3.0625 + -3.5y + y2 = -0.125 + 3.0625

Combine like terms: -0.125 + 3.0625 = 2.9375
3.0625 + -3.5y + y2 = 2.9375

Factor a perfect square on the left side:
(y + -1.75)(y + -1.75) = 2.9375

Calculate the square root of the right side: 1.71391365

Break this problem into two subproblems by setting 
(y + -1.75) equal to 1.71391365 and -1.71391365.


Subproblem 1
y + -1.75 = 1.71391365

Simplifying
y + -1.75 = 1.71391365

Reorder the terms:
-1.75 + y = 1.71391365

Solving
-1.75 + y = 1.71391365

Solving for variable 'y'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + y = 1.71391365 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + y = 1.71391365 + 1.75
y = 1.71391365 + 1.75

Combine like terms: 1.71391365 + 1.75 = 3.46391365
y = 3.46391365

Simplifying
y = 3.46391365


Subproblem 2
y + -1.75 = -1.71391365

Simplifying
y + -1.75 = -1.71391365

Reorder the terms:
-1.75 + y = -1.71391365

Solving
-1.75 + y = -1.71391365

Solving for variable 'y'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + y = -1.71391365 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + y = -1.71391365 + 1.75
y = -1.71391365 + 1.75

Combine like terms: -1.71391365 + 1.75 = 0.03608635
y = 0.03608635

Simplifying
y = 0.03608635


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.46391365, 0.03608635}
Solution
y = {3.46391365, 0.03608635}

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