Final answer:
To solve the equation (3x+3)(x+2)=1, we use the distributive property, rearrange the equation, and solve it using the quadratic formula. The solutions are x = (-15 + √165) / 6 and x = (-15 - √165) / 6.
Step-by-step explanation:
To solve the equation (3x+3)(x+2)=1, we can use the distributive property to expand the left side of the equation. This gives us 3x^2 + 9x + 6x + 6 = 1. Combining like terms, we get 3x^2 + 15x + 6 = 1. Rearranging the equation, we have 3x^2 + 15x + 5 = 0.
Next, we can solve this quadratic equation. We can use factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
Plugging in the values from our equation, we get x = (-15 ± √(15^2 - 4(3)(5))) / (2(3)). Simplifying further, we have x = (-15 ± √(225 - 60)) / 6. Continuing to simplify, we get x = (-15 ± √165) / 6. This gives us two possible values for x: x = (-15 + √165) / 6 and x = (-15 - √165) / 6.
Therefore, the solutions to the equation (3x+3)(x+2)=1 are x = (-15 + √165) / 6 and x = (-15 - √165) / 6.