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