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

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

Simplifying
2(x + 3) = 3(5x + -2)

Reorder the terms:
2(3 + x) = 3(5x + -2)
(3 * 2 + x * 2) = 3(5x + -2)
(6 + 2x) = 3(5x + -2)

Reorder the terms:
6 + 2x = 3(-2 + 5x)
6 + 2x = (-2 * 3 + 5x * 3)
6 + 2x = (-6 + 15x)

Solving
6 + 2x = -6 + 15x

Solving for variable 'x'.

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

Add '-15x' to each side of the equation.
6 + 2x + -15x = -6 + 15x + -15x

Combine like terms: 2x + -15x = -13x
6 + -13x = -6 + 15x + -15x

Combine like terms: 15x + -15x = 0
6 + -13x = -6 + 0
6 + -13x = -6

Add '-6' to each side of the equation.
6 + -6 + -13x = -6 + -6

Combine like terms: 6 + -6 = 0
0 + -13x = -6 + -6
-13x = -6 + -6

Combine like terms: -6 + -6 = -12
-13x = -12

Divide each side by '-13'.
x = 0.9230769231

Simplifying
x = 0.9230769231