(12x+ 18x² +21x +19) = (3x² + 3x)

x = (2 i)/sqrt(15) - 1 or x = -(2 i)/sqrt(15) - 1

Step-by-step explanation:

Solve for x:

18 x^2 + 33 x + 19 = 3 x (x + 1)

Expand out terms of the right hand side:

18 x^2 + 33 x + 19 = 3 x^2 + 3 x

Subtract 3 x^2 + 3 x from both sides:

15 x^2 + 30 x + 19 = 0

Divide both sides by 15:

x^2 + 2 x + 19/15 = 0

Subtract 19/15 from both sides:

x^2 + 2 x = -19/15

Add 1 to both sides:

x^2 + 2 x + 1 = -4/15

Write the left hand side as a square:

(x + 1)^2 = -4/15

Take the square root of both sides:

x + 1 = (2 i)/sqrt(15) or x + 1 = -(2 i)/sqrt(15)

Subtract 1 from both sides:

x = (2 i)/sqrt(15) - 1 or x + 1 = -(2 i)/sqrt(15)

Subtract 1 from both sides:

x = (2 i)/sqrt(15) - 1 or x = -(2 i)/sqrt(15) - 1

step-by-step explanation:

you divide the denominator by the numerator on both sides and if the quotients are equal then the fractions are equivalent