Solve for \( m \).

\((m+2)(m+3) = (m+2)(m-2)\)

( m + 2 ) ( m + 3 ) = ( m + 2 ) ( m − 2 ) m 2 + 3 m + 2 m + 6 = m 2 − 4 m 2 − m 2 + 5 m = − 4 − 6 5 m = − 10 / : 5 m = − 2

Answered by Anonymous | 2024-06-10

The first time you look at this, you would think that you can just cancel the (m+2) off of each side. But then you're left with (m+3) = (m-2), and there's no solution for this. So you have to go back and do it the hard way.
Expand each side of the equation. (Clear the parentheses.)
m² + 5m + 6 = m² - 4
Subtract m² from each side:
5m + 6 = -4
Subtract 6 from each side:
5m = -10
Divide each side by 5:
m = -2

Answered by AL2006 | 2024-06-10

The solution to the equation ( m + 2 ) ( m + 3 ) = ( m + 2 ) ( m − 2 ) is m = − 2 . By dividing both sides by m + 2 , we find that the assumption leads directly to the solution. Therefore, the complete solution is m = − 2 .
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Answered by Anonymous | 2025-02-27