Can someone tell me how to solve this example?

Question

(2p - 3)2 = 4(2p - 3) + 12

Answer 1

( 2p -3 ) 2= 4( 2p -3 ) +12

4p-6 = 8p -12+12

4 p - 6 = 8p

8p = 4p - 6

8p - 4p = - 6

Hence 4 p = - 6

4p = - 6 the answer

Answer 2

since you have like terms inside the parantheses, it becomes

-2(2p-3) =12

2p -3 = -6

2p =-3

p=- 3/2

Answer 3

(2p - 3)2 = 4(2p - 3) + 12

4p - 6 = 8p - 12 + 12

-6 = 4p

p = -3/2

Answer 4

Answer is :

1.) p = -3 / 2

Proof :

(2p - 3).2 = 4.(2p - 3) + 12

=> 4p - 6 = 8p - 12 + 12

=> p = -6 / 4 = -3 / 2

Proved.

Answer 5

(2p - 3)^2 = 4(2p - 3) + 12

(2p - 3)^2 – 4(2p - 3) – 12 = 0

Let (2p – 3) = x

x² – 4x – 12 = 0

(x – 6)(x + 2) = 0

x = 6 or x = – 2

2p – 3 = 6 or 2p – 3 = – 2

2p = 9 or 2p = 1

p = 9/2 or p = 1/2

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Answer 6

I've already seen three different answers.  So I suggest checking your solution by substitution back into the original.

4p - 6 = 8p - 12 + 12

-6 = 4p

p = -3/2

check: (2(-3/2) -3)*2 =? 4(2/(-3/2) - 3) + 12

(-3 - 3) * 2 =? 4(-3 - 3) + 12

-12 +? =? -24 + 12  <---yes, check!

- - - - -

If perchance the notation (2p - 3)2 represents (2p - 3) squared, then all bets are off.

Answer 7

solving for p, expand...=> 4p-6=8p-12+12

-4p=6

p=-2/3

Answer 8

expand both sides"

4p - 6 = 8p -12 + 12

add 6 to both sides

4p = 8p + 6

subtract 8 p from both sides

-4p = 6

divide both side by -4

p = -6/4 = -3/2