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

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


Simplifying
(y2 + 6)(-2y2 + 7) = 0

Reorder the terms:
(6 + y2)(-2y2 + 7) = 0

Reorder the terms:
(6 + y2)(7 + -2y2) = 0

Multiply (6 + y2) * (7 + -2y2)
(6(7 + -2y2) + y2(7 + -2y2)) = 0
((7 * 6 + -2y2 * 6) + y2(7 + -2y2)) = 0
((42 + -12y2) + y2(7 + -2y2)) = 0
(42 + -12y2 + (7 * y2 + -2y2 * y2)) = 0
(42 + -12y2 + (7y2 + -2y4)) = 0

Combine like terms: -12y2 + 7y2 = -5y2
(42 + -5y2 + -2y4) = 0

Solving
42 + -5y2 + -2y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(7 + -2y2)(6 + y2) = 0


Subproblem 1
Set the factor '(7 + -2y2)' equal to zero and attempt to solve:

Simplifying
7 + -2y2 = 0

Solving
7 + -2y2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2y2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2y2 = 0 + -7
-2y2 = 0 + -7

Combine like terms: 0 + -7 = -7
-2y2 = -7

Divide each side by '-2'.
y2 = 3.5

Simplifying
y2 = 3.5

Take the square root of each side:
y = {-1.870828693, 1.870828693}

Subproblem 2
Set the factor '(6 + y2)' equal to zero and attempt to solve:

Simplifying
6 + y2 = 0

Solving
6 + y2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + y2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + y2 = 0 + -6
y2 = 0 + -6

Combine like terms: 0 + -6 = -6
y2 = -6

Simplifying
y2 = -6

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
y = {-1.870828693, 1.870828693}

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