3(2x)=5(e^3x)

Solution for 3(2x)=5(e^3x) equation:

Simplifying
3(2x) = 5(e3x)

Remove parenthesis around (2x)
3 * 2x = 5(e3x)

Multiply 3 * 2
6x = 5(e3x)

Solving
6x = 5e3x

Solving for variable 'x'.

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

Add '-5e3x' to each side of the equation.
-5e3x + 6x = 5e3x + -5e3x

Combine like terms: 5e3x + -5e3x = 0
-5e3x + 6x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5e3 + 6) = 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 '(-5e3 + 6)' equal to zero and attempt to solve:

Simplifying
-5e3 + 6 = 0

Reorder the terms:
6 + -5e3 = 0

Solving
6 + -5e3 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5e3 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5e3 = 0 + -6
-5e3 = 0 + -6

Combine like terms: 0 + -6 = -6
-5e3 = -6

Add '5e3' to each side of the equation.
-5e3 + 5e3 = -6 + 5e3

Combine like terms: -5e3 + 5e3 = 0
0 = -6 + 5e3

Simplifying
0 = -6 + 5e3

The solution to this equation could not be determined.

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