(a-3)-a(a%2B5)%3D6.jpeg "(a+3)(a-3)-a(a+5)=6")
Solving the Equation: (a + 3)(a - 3) - a(a + 5) = 6
This article will walk you through the steps of solving the algebraic equation: (a + 3)(a - 3) - a(a + 5) = 6.
Step 1: Expanding the Equation
We start by expanding the equation using the distributive property:
- (a + 3)(a - 3) can be expanded as: a² - 3a + 3a - 9 = a² - 9
- a(a + 5) can be expanded as: a² + 5a
Substituting these expansions back into the original equation, we get:
(a² - 9) - (a² + 5a) = 6
Step 2: Simplifying the Equation
Next, we simplify the equation by combining like terms:
a² - 9 - a² - 5a = 6 -5a - 9 = 6
Step 3: Isolating the Variable
To isolate the variable 'a', we add 9 to both sides of the equation:
-5a - 9 + 9 = 6 + 9 -5a = 15
Step 4: Solving for 'a'
Finally, we divide both sides by -5 to find the value of 'a':
-5a / -5 = 15 / -5 a = -3
Therefore, the solution to the equation (a + 3)(a - 3) - a(a + 5) = 6 is a = -3.