3x(49x^2-16)(x^2+25)=0

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Solution for 3x(49x^2-16)(x^2+25)=0 equation: 


Simplifying
3x(49x2 + -16)(x2 + 25) = 0

Reorder the terms:
3x(-16 + 49x2)(x2 + 25) = 0

Reorder the terms:
3x(-16 + 49x2)(25 + x2) = 0

Multiply (-16 + 49x2) * (25 + x2)
3x(-16(25 + x2) + 49x2 * (25 + x2)) = 0
3x((25 * -16 + x2 * -16) + 49x2 * (25 + x2)) = 0
3x((-400 + -16x2) + 49x2 * (25 + x2)) = 0
3x(-400 + -16x2 + (25 * 49x2 + x2 * 49x2)) = 0
3x(-400 + -16x2 + (1225x2 + 49x4)) = 0

Combine like terms: -16x2 + 1225x2 = 1209x2
3x(-400 + 1209x2 + 49x4) = 0
(-400 * 3x + 1209x2 * 3x + 49x4 * 3x) = 0
(-1200x + 3627x3 + 147x5) = 0

Solving
-1200x + 3627x3 + 147x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-400 + 1209x2 + 49x4) = 0

Factor a trinomial.
3x((-25 + -1x2)(16 + -49x2)) = 0

Factor a difference between two squares.
3x((-25 + -1x2)((4 + 7x)(4 + -7x))) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-25 + -1x2)' equal to zero and attempt to solve:

Simplifying
-25 + -1x2 = 0

Solving
-25 + -1x2 = 0

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

Add '25' to each side of the equation.
-25 + 25 + -1x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -1x2 = 0 + 25
-1x2 = 0 + 25

Combine like terms: 0 + 25 = 25
-1x2 = 25

Divide each side by '-1'.
x2 = -25

Simplifying
x2 = -25

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(4 + 7x)' equal to zero and attempt to solve:

Simplifying
4 + 7x = 0

Solving
4 + 7x = 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 + 7x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7x = 0 + -4
7x = 0 + -4

Combine like terms: 0 + -4 = -4
7x = -4

Divide each side by '7'.
x = -0.5714285714

Simplifying
x = -0.5714285714

Subproblem 4
Set the factor '(4 + -7x)' equal to zero and attempt to solve:

Simplifying
4 + -7x = 0

Solving
4 + -7x = 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 + -7x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7x = 0 + -4
-7x = 0 + -4

Combine like terms: 0 + -4 = -4
-7x = -4

Divide each side by '-7'.
x = 0.5714285714

Simplifying
x = 0.5714285714
Solution
x = {0, -0.5714285714, 0.5714285714}

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