Step 1. Move all terms to one side.
\(3 x^{2} +7x-24-13x=0\)
Step 2. Simplify \(3 x^{2} +7x-24-13x=0\) to \(3 x^{2} -6x-24\)
\(3 x^{2} -6x-24=0\)
Step 3. Factor out the common term 3
\(3( x^{2} -2x-8)=0\)
Step 4. Factor \(x^{2} - 2^{x} -8\)
1. Ask: Which two numbers add up to -2 and multiply to -8?
2. Answer: -4 and 2
3. Rewrite the expression as \((x-4)(x+2):\)
\(3(x-4)(x+2)=0\)
Step 5. solve for \(x\)
1. Ask: When will \((x-4)(x+2)\) equal zero?
2. Answer: When \(x-4=0\) or \(x+2=0\)
3. Solve each of the 2 equations above:
\(x=4,2\)
Done! :) \(x=4,2\) is your answer.
