Use factoring to solve the equation. 8z^2=56z-96?

Question

Use factoring to solve the equation. 8z^2=56z-96?

Answer 1

8z² = 56z - 96

8z² - 56z + 96 = 0

z² - 7z + 12 = 0

(z - 4) (z - 3) = 0

z = 4, z = 3

Answer 2

Write  8z^2=56z-96 as 8 z^2 + 96 - 56 z=0

Now propose that

8 z^2 + 96 - 56 z = ( z-a) (cz -b) with a, b, and c numbers to determine. Expand the product on the right hand side and note that c has to be 8, and

a=56/c=7, finally

b=96/a=96/7.

Thtas it.

Answer 3

Transfer all the terms in the left side of the equation to equate to zero.

this will be:

8z^2 -56z +96 = 0

(2z - 8)(4z - 12)

Factor is (2z - 8)(4z - 12)

Answer 4

8z^2=56z-96

8z^2-56z+96=0

8*(z^2-7z+12)=0

8*(z-3)(z-4)=0

z=3 or z=4

Answer 5

8z^2=56z-96

8z^2 - 56z + 96 = 0

z^2 - 7z + 12 = 0 {divide thru by 8}

Factors of +12 that add to -7 are -3 & -4

(z - 3)(z - 4) = 0

z = 3, 4

Answer 6

why factoring; its easier to use the quadratic formula?!?  

Answer 7

First, arrange it to this form:

8z² - 56z + 96 = 0

Notice that all the terms are divisible by 8.  Divide both sides by 8:

z² - 7z + 12 = 0

When the first term is just z², then you have something of the form (z+a)(z+b) = z²-7z+12.

Since, when we multiply this out, we get z²+(a+b)z+abz, that means that a+b = -7 and ab = 12.  Guess factors of 12 that add up to -7.