Question

Solve the quadratic equation by factoring and show work: 6x²−x=15

Answer 1

`x_(1) = -(3)/(2) \\x_(2)=(5)/(3)`

Explanation:

`6x^(2) -x=15` move the constant to the left

`6x^(2) -x-15=0` write as a difference

`6x^(2) +9x-10x-15=0` factor the expressions

`3x *(2x+3)-5(2x+3)=0` factor the expression

`(2x+3) * (3x-5) = 0` split into possible cases

`2x+3=0\\3x-5=0` solve the equations

Answer 2

`(2x + 3)(3x - 5)`

Explanation:

Step 1: Subtract 15 from both sides

`6x^2 - x - 15 = 15 - 15`

`6x^2 - x - 15`

Step 2: Factor

`6x^2 - x - 15`

`(2x + 3)(3x - 5)`

Answer:
`(2x + 3)(3x - 5)`