(50-x^2)(4x^2-25)=0

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Solution for (50-x^2)(4x^2-25)=0 equation: 


Simplifying
(50 + -1x2)(4x2 + -25) = 0

Reorder the terms:
(50 + -1x2)(-25 + 4x2) = 0

Multiply (50 + -1x2) * (-25 + 4x2)
(50(-25 + 4x2) + -1x2 * (-25 + 4x2)) = 0
((-25 * 50 + 4x2 * 50) + -1x2 * (-25 + 4x2)) = 0
((-1250 + 200x2) + -1x2 * (-25 + 4x2)) = 0
(-1250 + 200x2 + (-25 * -1x2 + 4x2 * -1x2)) = 0
(-1250 + 200x2 + (25x2 + -4x4)) = 0

Combine like terms: 200x2 + 25x2 = 225x2
(-1250 + 225x2 + -4x4) = 0

Solving
-1250 + 225x2 + -4x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-50 + x2)(25 + -4x2) = 0

Factor a difference between two squares.
(-50 + x2)((5 + 2x)(5 + -2x)) = 0


Subproblem 1
Set the factor '(-50 + x2)' equal to zero and attempt to solve:

Simplifying
-50 + x2 = 0

Solving
-50 + x2 = 0

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

Add '50' to each side of the equation.
-50 + 50 + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + x2 = 0 + 50
x2 = 0 + 50

Combine like terms: 0 + 50 = 50
x2 = 50

Simplifying
x2 = 50

Take the square root of each side:
x = {-7.071067812, 7.071067812}

Subproblem 2
Set the factor '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 3
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-7.071067812, 7.071067812, -2.5, 2.5}

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