Answer:
Solution; x = - 2, x = 5
Explanation:
We are given the following equation 2x^2 + 2x + 12 = 3x^2 - x + 2;
2x^2 + 2x + 12 = 3x^2 - x + 2 ⇒ Subtract 2 from either side,
2x^2 + 2x + 10 = 3x^2 - x ⇒ Add x on either side,
2x^2 + 2x + 10 = 3x^2 ⇒ Subtract 3x^2 on either side, simplifying result,
- x^2 + 3x + 10 = 0 ⇒ Factor out common term - 1,
- ( x^2 - 3x - 10 ) = 0 ⇒ Break expression into groups,
- ( x^2 + 2x ) + ( - 5x - 10 ) = 0⇒ Factor x from x^2 + 2x , and - 5 from - 5x - 10,
- ( x( x + 2 ) ) - 5( x + 2 ) = 0 ⇒ Factor out common term x + 2,
- ( x + 2 )( x - 5 ) = 0 ⇒ Apply Zero Factor Principle,
x + 2 = 0, and x - 5 = 0 ⇒ Simplify,
Solution; x = - 2, x = 5