6(x+1)=3x(2+x)

Solution for 6(x+1)=3x(2+x) equation:

Simplifying
6(x + 1) = 3x(2 + x)

Reorder the terms:
6(1 + x) = 3x(2 + x)
(1 * 6 + x * 6) = 3x(2 + x)
(6 + 6x) = 3x(2 + x)
6 + 6x = (2 * 3x + x * 3x)
6 + 6x = (6x + 3x2)

Add '-6x' to each side of the equation.
6 + 6x + -6x = 6x + -6x + 3x2

Combine like terms: 6x + -6x = 0
6 + 0 = 6x + -6x + 3x2
6 = 6x + -6x + 3x2

Combine like terms: 6x + -6x = 0
6 = 0 + 3x2
6 = 3x2

Solving
6 = 3x2

Solving for variable 'x'.

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

Add '-3x2' to each side of the equation.
6 + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
6 + -3x2 = 0

Add '-6' to each side of the equation.
6 + -6 + -3x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -3x2 = 0 + -6
-3x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-3x2 = -6

Divide each side by '-3'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}