can someone please explain to me how to do this math problem? thank you.?

4x² + 7x = 2

4x² + 7x – 2 = 0

product of coefficient of 1st and last term = (4)(– 2) =8

find factors of – 8 such that their sum or difference is + 7

8 = 1 × 8 sum = 9 and difference = 7

8 = 4 × 2 sum = 6 and difference = 2

out of these 1 × 8 gives difference = 7

so 7x = +8x – x

4x² + 7x – 2 = 0

4x² + 8x – x – 2 = 0

4x(x + 2) – 1(x + 2) = 0

(4x – 1)(x + 2) = 0

(4x – 1) = 0 or (x + 2) = 0

x = 1/4 or x = – 2

9x² + 30x = – 16

9x² + 30x + 16 = 0

9x² + 24x + 6x + 16 = 0

3x(3x + 8) + 2(3x + 8) = 0

(3x + 2)(3x + 8) = 0

(3x + 2) = 0 or (3x + 8) = 0

x = – 2/3 or x = – 8/3

– 2x² + 12x – 16 = 0

– 2(x² – 6x + 8) = 0 divide by – 2

x² – 6x + 8 = 0

x² – 4x – 2x + 8 = 0

x(x – 4) – 2(x – 4) = 0

(x – 2)(x – 4) = 0

x = 2 or x = 4

go reverse way

roots are 4 and 5

so x = 4 or x = 5

therefore

(x – 4) = 0 or (x – 5) = 0

(x – 4)(x – 5) = 0

x(x – 5) – 4(x – 5) = 0

x² – 5x – 4x + 20 = 0

x² – 9x + 20 = 0

roots are 1/2 and 3

so x = 1/2 or x = 3

therefore

(x – 1/2) = 0 or (x – 3) = 0

(2x – 1)/2 = 0 (x – 5) = 0

(2x – 1) = 0 (x – 5) = 0

(2x – 1)(x – 5) = 0

2x (x – 5) – 1(x – 5) = 0

2x² – 10x – x + 5 = 0

2x² – 11x + 5 = 0

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1)

4x^2 + 7x - 2 = 0

(4x - 1)(x + 2)

x = 1/4 or -2

use the same method for rest of the problems

factoring is guess and check

that is incredibly comparable to any multiplication of binomials, basically you ought to keep in mind i is the sq. root of -a million, so i^2 = -a million: (4 - 6i)^2 = (4 - 6i)*(4 - 6i) = sixteen - 24i - 24i + 36i^2 = sixteen - 48i - 36 = 20 - 48i