(a) 9x²+18x=-5, 9x²+18x+5=0=(3x+5)(3x+1), x=-5/3 or -1/3.
(b) 4x²+10x+3=0,
x²+5x/2=-3/4,
x²+5x/2+25/16=25/16-3/4=13/16,
(x+5/4)²=13/16,
x+5/4=±√13/4,
x=-5/4+√13/4 or -5/4-√13/4.
(c) 3x²+4x+7=0,
x²+4x/3=-7/3,
x²+4x/3+4/9=4/9-7/3=-17/9,
(x+2/3)²=-17/9 for which there are only complex solutions:
x=-2/3±i√17/3.
(d) 4x²+12x-2x+4=-3x²+15=-2x.
Three equations are implied:
(i) 7x²+10x-11=0,
x=(-10±√(100+308))/14=(-10±2√102)/14.
(ii) 3x²-2x-15=0,
x=(2±√(4+180))/6=(1±√46)/3.
(iii) 4x²+12x+4=0=4(x²+3x+1),
x=(-3±√5)/2.
The “solutions” are inconsistent so there is no solution.