3x^2-18=-3x Solve quadric equation by factoring?

3x^2 - 18 = -3x

First, move all components to the left side of the equal sign

3x^2 + 3x - 18 = 0

Then factor by finding the common terms of factorization

(3x - 6) (x + 3) = 0

Then solve systematically

3x - 6 = 0
3x = 6
x= 2

x +3 = 0
x = -3

3x^2 - 18 = -3x
3x^2 + 3x - 18 = 0
(3x^2 + 3x - 18)/3 = 0/3
x^2 + x - 6 = 0
x^2 + 3x - 2x - 6 = 0
(x^2 + 3x) - (2x + 6) = 0
x(x + 3) - 2(x + 3) = 0
(x + 3)(x - 2) = 0

x + 3 = 0
x = -3

x - 2 = 0
x = 2

∴ x = -3 , 2

Re-arrange the eqation to :

3x^2 + 3x - 18 = 0

Use Decomposition : two numbers that when multiplied will be -54 and when added will be 3.

9 and -6 suite these conditions.

3x^2 - 6x + 9x -18 = 0

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

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

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

Therefore your two answers are x = 2 , -3

3x² - 18 = -3x
3x² + 3x - 18 = 0
x² + x - 6 = 0
(x+3)(x-2) = 0
x = -3 or x = 2

...........try it again!......

3x^2-18=-3x
x=[-3+-sqrt(9-4*3*(-18))]/6
x=(-3+-15)/6
x=2
x=-3

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

3x² + 3x - 18 = 0
x² + x - 6 = 0
(x + 3)(x - 2) = 0
x = - 3 , x = 2

3x^2+3x-18=0

3(x^2-x-6)=0

3(x-3)(x+2)=0
x=3;-2

Good luck!