5b^2(b^2+4)=28-11b^2

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Solution for 5b^2(b^2+4)=28-11b^2 equation: 


Simplifying
5b2(b2 + 4) = 28 + -11b2

Reorder the terms:
5b2(4 + b2) = 28 + -11b2
(4 * 5b2 + b2 * 5b2) = 28 + -11b2
(20b2 + 5b4) = 28 + -11b2

Solving
20b2 + 5b4 = 28 + -11b2

Solving for variable 'b'.

Reorder the terms:
-28 + 20b2 + 11b2 + 5b4 = 28 + -11b2 + -28 + 11b2

Combine like terms: 20b2 + 11b2 = 31b2
-28 + 31b2 + 5b4 = 28 + -11b2 + -28 + 11b2

Reorder the terms:
-28 + 31b2 + 5b4 = 28 + -28 + -11b2 + 11b2

Combine like terms: 28 + -28 = 0
-28 + 31b2 + 5b4 = 0 + -11b2 + 11b2
-28 + 31b2 + 5b4 = -11b2 + 11b2

Combine like terms: -11b2 + 11b2 = 0
-28 + 31b2 + 5b4 = 0

Factor a trinomial.
(-7 + -1b2)(4 + -5b2) = 0


Subproblem 1
Set the factor '(-7 + -1b2)' equal to zero and attempt to solve:

Simplifying
-7 + -1b2 = 0

Solving
-7 + -1b2 = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1b2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1b2 = 0 + 7
-1b2 = 0 + 7

Combine like terms: 0 + 7 = 7
-1b2 = 7

Divide each side by '-1'.
b2 = -7

Simplifying
b2 = -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 + -5b2)' equal to zero and attempt to solve:

Simplifying
4 + -5b2 = 0

Solving
4 + -5b2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5b2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5b2 = 0 + -4
-5b2 = 0 + -4

Combine like terms: 0 + -4 = -4
-5b2 = -4

Divide each side by '-5'.
b2 = 0.8

Simplifying
b2 = 0.8

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

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