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

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

Simplifying
3(x3 + 4x4) = -2(3x4 + -5x3)
(x3 * 3 + 4x4 * 3) = -2(3x4 + -5x3)
(3x3 + 12x4) = -2(3x4 + -5x3)

Reorder the terms:
3x3 + 12x4 = -2(-5x3 + 3x4)
3x3 + 12x4 = (-5x3 * -2 + 3x4 * -2)
3x3 + 12x4 = (10x3 + -6x4)

Solving
3x3 + 12x4 = 10x3 + -6x4

Solving for variable 'x'.

Reorder the terms:
3x3 + -10x3 + 12x4 + 6x4 = 10x3 + -6x4 + -10x3 + 6x4

Combine like terms: 3x3 + -10x3 = -7x3
-7x3 + 12x4 + 6x4 = 10x3 + -6x4 + -10x3 + 6x4

Combine like terms: 12x4 + 6x4 = 18x4
-7x3 + 18x4 = 10x3 + -6x4 + -10x3 + 6x4

Reorder the terms:
-7x3 + 18x4 = 10x3 + -10x3 + -6x4 + 6x4

Combine like terms: 10x3 + -10x3 = 0
-7x3 + 18x4 = 0 + -6x4 + 6x4
-7x3 + 18x4 = -6x4 + 6x4

Combine like terms: -6x4 + 6x4 = 0
-7x3 + 18x4 = 0

Factor out the Greatest Common Factor (GCF), 'x3'.
x3(-7 + 18x) = 0

Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-7 + 18x)' equal to zero and attempt to solve:

Simplifying
-7 + 18x = 0

Solving
-7 + 18x = 0

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

Add '7' to each side of the equation.
-7 + 7 + 18x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 18x = 0 + 7
18x = 0 + 7

Combine like terms: 0 + 7 = 7
18x = 7

Divide each side by '18'.
x = 0.3888888889

Simplifying
x = 0.3888888889
Solution
x = {0.3888888889}