Solving Eqautions and Factoring

Solve Equations

x sqaured + 5x + 6=0

3x-7x sqaured = 0



Factoring
4x sqaured - 4x-3


(x+4) (x+6)+ ( x-9) (6-x)

1.) x²+5x+6 = 0
(x+2)(x+3) = 0

x+2 = 0 or x+3 = 0
x = -2 or x = -3
Solutions: x = -3 or x = -2

2.) 3x-7x² = 0
-x(7x-3) = 0

-x = 0 or 7x-3 = 0
x = 0 or 7x = 3
x = 0 or x = 3/7
Solutions: x = 0 or x = 3/7

3.) 4x²-4x-3 → (2x-3)(2x+1)

4.) (x+4)(x+6)+(x-9)(6-x) → 5(5x-6)

x^2 + 5x + 6 = 0
(x+3) (x+2) = 0
x= -2, -3

3x - 7x^2 = 0
x (3 - 7x) = 0
x= 0, 3/7

4x^2 - 4x - 3
= (2x + 1) (2x - 3)

(x + 4) (x + 6) - (x - 9) (x - 6)
= x^2 + 10x + 24 - (x^2 -15x + 54)
= 25x - 30
= 5 (5x - 6)

x²+5x-6=0
(x-1)(x+6)=0
x=1
x=-6

3x-7x²=0
x(3-7x)=0
x=0
3-7x=0
7x=3
x=3/7

4x²-4x-3=0
(2x-3)(2x+1)=0
2x=3
x=3/2
2x+1=0
2x=-1
x=-1/2