Factorising Quadratic Equations

Question

Factorise \(2x^2 - 12 + 4x = x^2 + 3x\)

Solution

Show solution Hide solution Fully worked — 4 steps

1. 1
   Add \(-x^2 - 3x\) to both sides

   \[ 2x^2 - 12 + 4x = x^2 + 3x \]

   \[ x^2 + x - 12 = 0 \]
2. 2
   Factorise

   \[ (x + 4)(x - 3) = 0 \]
3. 3
   Using the zero-factor theorem, equate each factor to 0

   Then either

   \[ x + 4 = 0 \Rightarrow x = -4 \]

   or

   \[ x - 3 = 0 \Rightarrow x = 3 \]
4. State the solutions

   The solutions are \(x = -4\) or \(x = 3\). That is, \(x\) is minus four and \(x\) is three.