What are the roots of the equation 3x^2 + 6x = x^2 - 4x

Expert Answers
justaguide eNotes educator| Certified Educator

The roots of the equation 3x^2 + 6x = x^2 - 4x have to be determined.

3x^2 + 6x = x^2 - 4x

=> 3x^2 - x^2 + 6x + 4x = 0

=> 2x^2 + 10x = 0

=> x(2x + 10) = 0

=> x = 0 and x = -10/2 = -5

The roots of the equation 3x^2 + 6x = x^2 - 4x are 0 and -5

givingiswinning | Student

3x^2 + 6x = x^2 - 4x

move termsĀ 

3x^2 - x^2 + 6x + 4x = 0

simplify

2x^2 + 10x = 0

factor out:

2x(x + 5) = 0

set equal to 0:

2x = 0

x=0

x + 5 = 0

x = -5

The roots are 0 and -5

atyourservice | Student

The roots of the equation 3x^2 + 6x = x^2 - 4x have to be determined.

3x^2 + 6x = x^2 - 4x

move terms to the same side:

3x^2 - x^2 + 6x + 4x = 0

now simplify, by combining terms:

2x^2 + 10x = 0

they both have x and 2 as a greatest common factor so factor those out:

2x(x + 5) = 0

set them equal to 0:

2x = 0

  • x=0

x + 5 = 0

  • x = -5

The roots are 0 and -5