Solving Quadratic Equations by Factoring

Already Factored

100

(x+3)(x-7)=0

x=-3, x=7

200

(x+4)(x+18)=0

x=-4, x=-18

300

(2x-7)(3x+9)=0

x=7/2, x=-3

400

n(3n+5)=0

n=0, n=-5/3

500

a(a-5)=0

a=0, a=5

Leading Coefficient of 1

100

m²+2m-3=0

x=1 or x=-3

200

v²-7v+6=0

v=1 or v=6

300

x²-x-12=0

x=-3 or x=4

400

r²+9r+12=2r

r=-4 or r=-3

500

p²-9p+17=-3

p=5 or p=4

Leading Coefficient >1

100

2x²-x-15=0

x=-5/2, x=3

200

3x²-11x +8=0

x=8/3 and x=1

300

9x²+6x=0

x=0 or x=-2/3

400

3x²+10x-25=0

x=5/3, x=-5

500

7x²-30x-24=8x

x=-4/7, x=6

Special Cases

100

n² -16=0

n=4 or n=-4

200

p²-4p+1=-3

p=2

300

4x²-12x+9=0

x=3/2

400

25m²-9=0

n=3/5 or n=-3/5

500

16x²-40x+25=0

n=5/4

Equation from Roots

100

r=-5/3, r=0

3r²+5r=0

200

n=-6, n=-7

n²+13n+42=0

300

v=8, v=15

v²-23v+120=0

400

x=-8/7, x=-2

7x²+22x+16=0

500

x=8/3, x=3/5

15x²-49x+24=0