(-7y^2+4y+6)=(7y^2-4y+4)-(2y^2-2y-6)

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Solution for (-7y^2+4y+6)=(7y^2-4y+4)-(2y^2-2y-6) equation:


Simplifying
(-7y2 + 4y + 6) = (7y2 + -4y + 4) + -1(2y2 + -2y + -6)

Reorder the terms:
(6 + 4y + -7y2) = (7y2 + -4y + 4) + -1(2y2 + -2y + -6)

Remove parenthesis around (6 + 4y + -7y2)
6 + 4y + -7y2 = (7y2 + -4y + 4) + -1(2y2 + -2y + -6)

Reorder the terms:
6 + 4y + -7y2 = (4 + -4y + 7y2) + -1(2y2 + -2y + -6)

Remove parenthesis around (4 + -4y + 7y2)
6 + 4y + -7y2 = 4 + -4y + 7y2 + -1(2y2 + -2y + -6)

Reorder the terms:
6 + 4y + -7y2 = 4 + -4y + 7y2 + -1(-6 + -2y + 2y2)
6 + 4y + -7y2 = 4 + -4y + 7y2 + (-6 * -1 + -2y * -1 + 2y2 * -1)
6 + 4y + -7y2 = 4 + -4y + 7y2 + (6 + 2y + -2y2)

Reorder the terms:
6 + 4y + -7y2 = 4 + 6 + -4y + 2y + 7y2 + -2y2

Combine like terms: 4 + 6 = 10
6 + 4y + -7y2 = 10 + -4y + 2y + 7y2 + -2y2

Combine like terms: -4y + 2y = -2y
6 + 4y + -7y2 = 10 + -2y + 7y2 + -2y2

Combine like terms: 7y2 + -2y2 = 5y2
6 + 4y + -7y2 = 10 + -2y + 5y2

Solving
6 + 4y + -7y2 = 10 + -2y + 5y2

Solving for variable 'y'.

Reorder the terms:
6 + -10 + 4y + 2y + -7y2 + -5y2 = 10 + -2y + 5y2 + -10 + 2y + -5y2

Combine like terms: 6 + -10 = -4
-4 + 4y + 2y + -7y2 + -5y2 = 10 + -2y + 5y2 + -10 + 2y + -5y2

Combine like terms: 4y + 2y = 6y
-4 + 6y + -7y2 + -5y2 = 10 + -2y + 5y2 + -10 + 2y + -5y2

Combine like terms: -7y2 + -5y2 = -12y2
-4 + 6y + -12y2 = 10 + -2y + 5y2 + -10 + 2y + -5y2

Reorder the terms:
-4 + 6y + -12y2 = 10 + -10 + -2y + 2y + 5y2 + -5y2

Combine like terms: 10 + -10 = 0
-4 + 6y + -12y2 = 0 + -2y + 2y + 5y2 + -5y2
-4 + 6y + -12y2 = -2y + 2y + 5y2 + -5y2

Combine like terms: -2y + 2y = 0
-4 + 6y + -12y2 = 0 + 5y2 + -5y2
-4 + 6y + -12y2 = 5y2 + -5y2

Combine like terms: 5y2 + -5y2 = 0
-4 + 6y + -12y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 3y + -6y2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-2 + 3y + -6y2)' equal to zero and attempt to solve: Simplifying -2 + 3y + -6y2 = 0 Solving -2 + 3y + -6y2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 0.3333333333 + -0.5y + y2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -0.5y + -0.3333333333 + y2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -0.5y + y2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -0.5y + y2 = 0 + -0.3333333333 -0.5y + y2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -0.5y + y2 = -0.3333333333 The y term is -0.5y. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5y + 0.0625 + y2 = -0.3333333333 + 0.0625 Reorder the terms: 0.0625 + -0.5y + y2 = -0.3333333333 + 0.0625 Combine like terms: -0.3333333333 + 0.0625 = -0.2708333333 0.0625 + -0.5y + y2 = -0.2708333333 Factor a perfect square on the left side: (y + -0.25)(y + -0.25) = -0.2708333333 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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