To find the value of 'a', expand the right side of the equation:
(x+6)(x-a) = x^2 - ax + 6x - 6= x^2 - (a-6)x - 6a
Now, we can set the expanded form equal to the original equation:
x^2 + 13x + 42 = x^2 - (a-6)x - 6a
Now we can compare the coefficients on both sides:
13 = -(a-6) (coefficients of x42 = -6a (constant term)
From first equation, we get13 = -a + a = 6 - 1a = -7
So, the value of 'a' is -7.
To find the value of 'a', expand the right side of the equation:
(x+6)(x-a) = x^2 - ax + 6x - 6
= x^2 - (a-6)x - 6a
Now, we can set the expanded form equal to the original equation:
x^2 + 13x + 42 = x^2 - (a-6)x - 6a
Now we can compare the coefficients on both sides:
13 = -(a-6) (coefficients of x
42 = -6a (constant term)
From first equation, we get
13 = -a +
a = 6 - 1
a = -7
So, the value of 'a' is -7.