factor 4z^2=76z-336?

4z^2 = 76z - 336

4*(z^2 - 19z + 84) = 0.

4*(x - 7)(x - 12) = 0.

x = 7 and x = 12.

-John

4z² = 76z - 336
z² = 19z - 84
z² - 19z = - 84
z² - (19 - 1/2[19])z = - 84 + (1/2[19])²
z² - (19 - 19/2)z = - 84 + (19/2)²
z² - (38/2 - 19/2)z = - 84 + 361/4
z² - 19/2z = - 336/4 + 361/4
(z - 19/2)² = - 25/4
z - 19/2 = - 5/2

1st value of z:
z - 19/2 = - 5/2
z = - 5/2 + 19/2
z = 14/2 or 7

2nd value of z:
z - 19/2 - 5/2 = 0
z - 24/2 = 0
z - 12 = 0
z = 12

Proof where z is 7:
4(7²) = 76(7) - 336
4(49) = 532 - 336
196 = 196

Proof where z is 12:
4(12²) = 76(12) - 336
4(144) = 912 - 336
576 = 576

4z^2 = 76z - 336
4z^2 - 76z + 336 = 0
(4z^2 - 76z + 336)/4 = 0/4
z^2 - 19z + 84 = 0
(z - 7)(z - 12) = 0

z - 7 = 0
z = 7

z - 12 = 0
z = 12

∴ z = 7 , 12

divide eqn by 4
z^2-19z-84=0

sol z= 12, z= 9

4z^2-76z+336=0

4(z^2-19z+84)=0

4(z-7)(z-12)=0
z=7 and 12

z² - 19z + 84 = 0
(z - 12)(z - 7) = 0
z = 12 , z = 7

4z^2=76z-336
=>4z^2-76z+336=0
=>z^2-19z+84=0
=>z^2-12z-7z+84=0
=>z(z-12)-7(z-12)=0
=>(z-12)(z-7)=0
hence (z-12)=0 and (z-7)=0
i.e, z=12 and 7