What is the value of x in: 2/3(x+6)=-18

For this equation:

Rearrange:

2/3*(x+6)-(-18)=0 

Equation at the end of step 1:

(2/3*(x+6))-(-18)=0

Equation at the end of step 2:

2*(x+6)/3-(-18)=0

Rewriting the whole as an Equivalent Fraction:

-18=-18/1=-18*3/3

Adding fractions that have a common denominator:

2 • (x+6) - (-18 • 3)/3 = 2x + 66/3

Pulling out like terms:

2x + 66  =   2 • (x + 33) 

Equation at the end of step 4:

2 • (x + 33)/3 = 0

When a fraction equals zero:

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now, to get rid of the denominator, multiply both sides of the equation by the denominator.

Here's how:

2•(x+33)/3 * 3=0*3

Now, on the left hand side, the  3  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

2  •  (x+33)  = 0

Equations which are never true:

Solve :    2   =  0

This equation has no solution.
A a non-zero constant never equals zero.

Solving a Single Variable Equation:

Solve: x+33 = 0 

Subtract  33  from both sides of the equation : x = -33 

Final X = -33