(4x^2-1)(25-x^2)=0

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Solution for (4x^2-1)(25-x^2)=0 equation: 


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

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

Multiply (-1 + 4x2) * (25 + -1x2)
(-1(25 + -1x2) + 4x2 * (25 + -1x2)) = 0
((25 * -1 + -1x2 * -1) + 4x2 * (25 + -1x2)) = 0
((-25 + 1x2) + 4x2 * (25 + -1x2)) = 0
(-25 + 1x2 + (25 * 4x2 + -1x2 * 4x2)) = 0
(-25 + 1x2 + (100x2 + -4x4)) = 0

Combine like terms: 1x2 + 100x2 = 101x2
(-25 + 101x2 + -4x4) = 0

Solving
-25 + 101x2 + -4x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-25 + x2)(1 + -4x2) = 0

Factor a difference between two squares.
((5 + x)(-5 + x))(1 + -4x2) = 0

Factor a difference between two squares.
((1 + 2x)(1 + -2x))(5 + x)(-5 + x) = 0


Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

Simplifying
x = -5

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

Simplifying
-5 + x = 0

Solving
-5 + x = 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 + x = 0 + 5

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

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

Simplifying
x = 5

Subproblem 3
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 4
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-5, 5, -0.5, 0.5}

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