Identify the roots of the equation and the multiplicities of the roots.
(x - 6)(x + 4)2 = 0

Roots are x=6 and - 4

Step-by-step explanation:

2(x-6)(x+4)=0

(x-6)=0 or (x+4)=0

x=6 or x=-4, their multiplicities is 1

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions