Question

Perform the operation(s) and simplify completely
-(2x +6) (3x +4) = 5x^2 - 7x

Answer 1

To simplify the equation \(- (2x + 6)(3x + 4) = 5x^2 - 7x\), we need to first expand the left side and then combine like terms.

1. Expand the left side:
\[
- (2x + 6)(3x + 4)
\]
First, calculate \((2x + 6)(3x + 4)\) using the distributive property (also known as the FOIL method for binomials):
\[
2x \cdot 3x + 2x \cdot 4 + 6 \cdot 3x + 6 \cdot 4
\]
This simplifies to:
\[
6x^2 + 8x + 18x + 24 = 6x^2 + 26x + 24
\]

Now, applying the negative sign:
\[
- (6x^2 + 26x + 24) = -6x^2 - 26x - 24
\]

2. Now we have the equation:
\[
-6x^2 - 26x - 24 = 5x^2 - 7x
\]

3. To bring all terms to one side, add \(6x^2 + 26x + 24\) to both sides:
\[
0 = 5x^2 - 7x + 6x^2 + 26x + 24
\]

Combining like terms:
\[
0 = (5x^2 + 6x^2) + (-7x + 26x) + 24
\]
\[
0 = 11x^2 + 19x + 24
\]

4. Rearrange it:
\[
11x^2 + 19x + 24 = 0
\]

The simplified expression for the left side gives us a quadratic equation:
\[
11x^2 + 19x + 24 = 0
\]

To summarize, the final result is:
\[
11x^2 + 19x + 24 = 0
\]