How do you solve 4x^2-12x=7 algebraically

(if you don't wanna read all this the answer is at the bottom btw)

move the 7 over to equate the equation to 0

4x^2 - 12x -7 = 0

(ok now you have a (4), b (-12), and c (-7) here you can either use the quadratic formula to solve it or factor the equation)

to factor it, you have to multiply a and c (4*-7 = -28) and find two numbers that multiply to -28 and add to -12

the numbers are -14 and 2. sub those into the equation in place of b

4x^2 + 2x - 14x - 7 = 0

find the lcd of the first two terms and the last two terms to factor them

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

to find the two x values you need to find what values make the equation equal 0 on both sides.

so x is 7/2 or -1/2