(2x+3)(x-7)=4(x-7)?

Answer 1

(2x + 3) (x-7) = 4(x-7)
First we need to multiply out the left hand side

==>2x*x + (2x)*(-7) + 3*x +3*(-7) = 4x +4*(-7)
Clean things up a little bit:
==>2x^2 -14x +3x -21 = 4x -28
Combining some like terms:
==>2x^2 -11x -21 = 4x -28

Now, subtract the (4x - 28) from both sides:

==>2x^2 -11x -21 - (4x - 28) = 4x -28 - (4x - 28)

Simplifying a little:
==>2x^2 -11x - 21 -4x +28 = 0

Combine like terms:
==>2x^2 -15x + 7 = 0

Factor this:

(2x - 1)(x - 7) = 0

This gives that

2x-1 = 0 ==> x = 1/2
and
x-7=0 ==> x = 7

I'm a mathematician, so if you need, please ask for further help.

Also, there's a quick way to do this problem:
(2x+3)(x-7) = 4(x-7)
==> (2x+3)(x-7) -4(x-7) = 0

Factor out the (x-7)
==> (x-7)(2x+3 -4) = 0
==> (x-7)(2x-1)=0 and we're done!

Answer 2

I shall sove it easier
either x-7 = 0 means x = 7

or deviding both sides by x-7

2x+3 = 4 means x = 1/2

Answer 3

Multiply everything to get:

2x²-14x=3x-21 = 4x-28

than simplify to :
2x² - 15x =7 =0

Find the Squares:
[two numbers the when inserted to (2x-?)(x-?) will multiply to get 7 and add to get -15]

(2x-1)=0 (x-7)=0
x= ½ x=7

Answer 4

(2x+3)(x-7)=4(x-7)
2x^2-14x+3x-21=4x -28
2x^2-15x+7=0
(2x-1)(x-7)=0
x=1/2 or 7

Answer 5

x = 6.02 X 10 ^ 23
OR
x = 3.1415926......