(4x^2+7x)(25x^2-5x-2)=0

Solution for (4x^2+7x)(25x^2-5x-2)=0 equation:

Simplifying
(4x2 + 7x)(25x2 + -5x + -2) = 0

Reorder the terms:
(7x + 4x2)(25x2 + -5x + -2) = 0

Reorder the terms:
(7x + 4x2)(-2 + -5x + 25x2) = 0

Multiply (7x + 4x2) * (-2 + -5x + 25x2)
(7x * (-2 + -5x + 25x2) + 4x2 * (-2 + -5x + 25x2)) = 0
((-2 * 7x + -5x * 7x + 25x2 * 7x) + 4x2 * (-2 + -5x + 25x2)) = 0
((-14x + -35x2 + 175x3) + 4x2 * (-2 + -5x + 25x2)) = 0
(-14x + -35x2 + 175x3 + (-2 * 4x2 + -5x * 4x2 + 25x2 * 4x2)) = 0
(-14x + -35x2 + 175x3 + (-8x2 + -20x3 + 100x4)) = 0

Reorder the terms:
(-14x + -35x2 + -8x2 + 175x3 + -20x3 + 100x4) = 0

Combine like terms: -35x2 + -8x2 = -43x2
(-14x + -43x2 + 175x3 + -20x3 + 100x4) = 0

Combine like terms: 175x3 + -20x3 = 155x3
(-14x + -43x2 + 155x3 + 100x4) = 0

Solving
-14x + -43x2 + 155x3 + 100x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-14 + -43x + 155x2 + 100x3) = 0

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 '(-14 + -43x + 155x2 + 100x3)' equal to zero and attempt to solve:

Simplifying
-14 + -43x + 155x2 + 100x3 = 0

Solving
-14 + -43x + 155x2 + 100x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}