Solve (3x+4)(x+2)=3x²+2 Using the Distributive Property

To solve the equation $(3x+4)(x+2) = 3x^2 + 2$, we start by expanding the left-hand side using the distributive property.

First, distribute each component of the first polynomial:

$(3x+4)(x+2) = 3x(x+2) + 4(x+2)$

Next, distribute inside each term:

$3x(x+2) = 3x \cdot x + 3x \cdot 2 = 3x^2 + 6x$$4(x+2) = 4 \cdot x + 4 \cdot 2 = 4x + 8$

Combining these, we have:

$3x^2 + 6x + 4x + 8 = 3x^2 + 10x + 8$

Set the expanded expression equal to the right side of the original equation:

$3x^2 + 10x + 8 = 3x^2 + 2$

To solve for $x$, subtract $3x^2$ from both sides:

$10x + 8 = 2$

Next, subtract 8 from both sides to isolate the term involving $x$:

$10x = 2 - 8$

$10x = -6$

Finally, divide both sides by 10:

$x = \frac{-6}{10}$$x = -0.6$

Therefore, the solution to the equation is $-0.6$.

The correct choice from the provided options is $\boxed{-0.6}$.