(a^2+1)a^2-7(a^2+1)=0

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Solution for (a^2+1)a^2-7(a^2+1)=0 equation: 


Simplifying
(a2 + 1) * a2 + -7(a2 + 1) = 0

Reorder the terms:
(1 + a2) * a2 + -7(a2 + 1) = 0

Reorder the terms for easier multiplication:
a2(1 + a2) + -7(a2 + 1) = 0
(1 * a2 + a2 * a2) + -7(a2 + 1) = 0
(1a2 + a4) + -7(a2 + 1) = 0

Reorder the terms:
1a2 + a4 + -7(1 + a2) = 0
1a2 + a4 + (1 * -7 + a2 * -7) = 0
1a2 + a4 + (-7 + -7a2) = 0

Reorder the terms:
-7 + 1a2 + -7a2 + a4 = 0

Combine like terms: 1a2 + -7a2 = -6a2
-7 + -6a2 + a4 = 0

Solving
-7 + -6a2 + a4 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1 + -1a2)(7 + -1a2) = 0


Subproblem 1
Set the factor '(-1 + -1a2)' equal to zero and attempt to solve:

Simplifying
-1 + -1a2 = 0

Solving
-1 + -1a2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1a2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1a2 = 0 + 1
-1a2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1a2 = 1

Divide each side by '-1'.
a2 = -1

Simplifying
a2 = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(7 + -1a2)' equal to zero and attempt to solve:

Simplifying
7 + -1a2 = 0

Solving
7 + -1a2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1a2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a2 = 0 + -7
-1a2 = 0 + -7

Combine like terms: 0 + -7 = -7
-1a2 = -7

Divide each side by '-1'.
a2 = 7

Simplifying
a2 = 7

Take the square root of each side:
a = {-2.645751311, 2.645751311}
Solution
a = {-2.645751311, 2.645751311}

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