4x^2(2x^3+4x-5)-6x^3(x^2-3)=

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Solution for 4x^2(2x^3+4x-5)-6x^3(x^2-3)= equation: 


Simplifying
4x2(2x3 + 4x + -5) + -6x3(x2 + -3) = 0

Reorder the terms:
4x2(-5 + 4x + 2x3) + -6x3(x2 + -3) = 0
(-5 * 4x2 + 4x * 4x2 + 2x3 * 4x2) + -6x3(x2 + -3) = 0
(-20x2 + 16x3 + 8x5) + -6x3(x2 + -3) = 0

Reorder the terms:
-20x2 + 16x3 + 8x5 + -6x3(-3 + x2) = 0
-20x2 + 16x3 + 8x5 + (-3 * -6x3 + x2 * -6x3) = 0
-20x2 + 16x3 + 8x5 + (18x3 + -6x5) = 0

Reorder the terms:
-20x2 + 16x3 + 18x3 + 8x5 + -6x5 = 0

Combine like terms: 16x3 + 18x3 = 34x3
-20x2 + 34x3 + 8x5 + -6x5 = 0

Combine like terms: 8x5 + -6x5 = 2x5
-20x2 + 34x3 + 2x5 = 0

Solving
-20x2 + 34x3 + 2x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(-10 + 17x + x3) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(-10 + 17x + x3)' equal to zero and attempt to solve:

Simplifying
-10 + 17x + x3 = 0

Solving
-10 + 17x + x3 = 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}

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