To factor this quadratic equation, we can use the quadratic formula. The formula states that for a quadratic equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, the values for a, b, and c are:

a = 1
b = -(8+6i)
c = 7 + 16i

Now we can substitute these values into the formula to find the solutions for x:

x = [-(8+6i) ± √((8+6i)^2 - 41(7+16i))] / 2*1

Expand the equation under the square root:

x = [-(8+6i) ± √(64 + 96i + 36 - 28 - 64i)] / 2

Simplify the square root:

x = [-(8+6i) ± √(72 + 32i)] / 2

Now we have the two possible solutions for x:

x = (8+6i ± √(72 + 32i)) / 2