5x^2(x^2+3)=28-16x^2

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Solution for 5x^2(x^2+3)=28-16x^2 equation: 


Simplifying
5x2(x2 + 3) = 28 + -16x2

Reorder the terms:
5x2(3 + x2) = 28 + -16x2
(3 * 5x2 + x2 * 5x2) = 28 + -16x2
(15x2 + 5x4) = 28 + -16x2

Solving
15x2 + 5x4 = 28 + -16x2

Solving for variable 'x'.

Reorder the terms:
-28 + 15x2 + 16x2 + 5x4 = 28 + -16x2 + -28 + 16x2

Combine like terms: 15x2 + 16x2 = 31x2
-28 + 31x2 + 5x4 = 28 + -16x2 + -28 + 16x2

Reorder the terms:
-28 + 31x2 + 5x4 = 28 + -28 + -16x2 + 16x2

Combine like terms: 28 + -28 = 0
-28 + 31x2 + 5x4 = 0 + -16x2 + 16x2
-28 + 31x2 + 5x4 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-28 + 31x2 + 5x4 = 0

Factor a trinomial.
(-7 + -1x2)(4 + -5x2) = 0


Subproblem 1
Set the factor '(-7 + -1x2)' equal to zero and attempt to solve:

Simplifying
-7 + -1x2 = 0

Solving
-7 + -1x2 = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x2 = 0 + 7
-1x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-1x2 = 7

Divide each side by '-1'.
x2 = -7

Simplifying
x2 = -7

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 '(4 + -5x2)' equal to zero and attempt to solve:

Simplifying
4 + -5x2 = 0

Solving
4 + -5x2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x2 = 0 + -4
-5x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-5x2 = -4

Divide each side by '-5'.
x2 = 0.8

Simplifying
x2 = 0.8

Take the square root of each side:
x = {-0.894427191, 0.894427191}
Solution
x = {-0.894427191, 0.894427191}

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