(2x+5)(2x-5)(4x^2+25)=0

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Solution for (2x+5)(2x-5)(4x^2+25)=0 equation: 


Simplifying
(2x + 5)(2x + -5)(4x2 + 25) = 0

Reorder the terms:
(5 + 2x)(2x + -5)(4x2 + 25) = 0

Reorder the terms:
(5 + 2x)(-5 + 2x)(4x2 + 25) = 0

Reorder the terms:
(5 + 2x)(-5 + 2x)(25 + 4x2) = 0

Multiply (5 + 2x) * (-5 + 2x)
(5(-5 + 2x) + 2x * (-5 + 2x))(25 + 4x2) = 0
((-5 * 5 + 2x * 5) + 2x * (-5 + 2x))(25 + 4x2) = 0
((-25 + 10x) + 2x * (-5 + 2x))(25 + 4x2) = 0
(-25 + 10x + (-5 * 2x + 2x * 2x))(25 + 4x2) = 0
(-25 + 10x + (-10x + 4x2))(25 + 4x2) = 0

Combine like terms: 10x + -10x = 0
(-25 + 0 + 4x2)(25 + 4x2) = 0
(-25 + 4x2)(25 + 4x2) = 0

Multiply (-25 + 4x2) * (25 + 4x2)
(-25(25 + 4x2) + 4x2 * (25 + 4x2)) = 0
((25 * -25 + 4x2 * -25) + 4x2 * (25 + 4x2)) = 0
((-625 + -100x2) + 4x2 * (25 + 4x2)) = 0
(-625 + -100x2 + (25 * 4x2 + 4x2 * 4x2)) = 0
(-625 + -100x2 + (100x2 + 16x4)) = 0

Combine like terms: -100x2 + 100x2 = 0
(-625 + 0 + 16x4) = 0
(-625 + 16x4) = 0

Solving
-625 + 16x4 = 0

Solving for variable 'x'.

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

Add '625' to each side of the equation.
-625 + 625 + 16x4 = 0 + 625

Combine like terms: -625 + 625 = 0
0 + 16x4 = 0 + 625
16x4 = 0 + 625

Combine like terms: 0 + 625 = 625
16x4 = 625

Divide each side by '16'.
x4 = 39.0625

Simplifying
x4 = 39.0625

Reorder the terms:
-39.0625 + x4 = 39.0625 + -39.0625

Combine like terms: 39.0625 + -39.0625 = 0.0000
-39.0625 + x4 = 0.0000

Factor a difference between two squares.
(6.25 + x2)(-6.25 + x2) = 0.0000

Factor a difference between two squares.
(6.25 + x2)((2.5 + x)(-2.5 + x)) = 0.0000


Subproblem 1
Set the factor '(6.25 + x2)' equal to zero and attempt to solve:

Simplifying
6.25 + x2 = 0

Solving
6.25 + x2 = 0

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

Add '-6.25' to each side of the equation.
6.25 + -6.25 + x2 = 0 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + x2 = 0 + -6.25
x2 = 0 + -6.25

Combine like terms: 0 + -6.25 = -6.25
x2 = -6.25

Simplifying
x2 = -6.25

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 '(2.5 + x)' equal to zero and attempt to solve:

Simplifying
2.5 + x = 0

Solving
2.5 + x = 0

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 0 + -2.5
x = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
x = -2.5

Simplifying
x = -2.5

Subproblem 3
Set the factor '(-2.5 + x)' equal to zero and attempt to solve:

Simplifying
-2.5 + x = 0

Solving
-2.5 + x = 0

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 0 + 2.5
x = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
x = 2.5

Simplifying
x = 2.5
Solution
x = {-2.5, 2.5}

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