Question

Solve using the method of your choice: (3x+10)(x+2)=3(x+5)+15 ?

Answer 1

1. Expand both sides
2. Simplify like terms
3. Move all terms to one side and use the null factor law to solve for `x`

Explanation:

Expanding brackets
`3x^2 + 6x +10x+20=3x+15+15`

Simplifying like terms
`3x^2+16x+20=3x+30`

Moving terms to left hand side
`3x^2 +16x +20 -3x -30 =0`
`3x^2 +13x -10=0`

Split the middle term to factorise
`3x^2 +15x-2x-10=0`
`3x(x+5)-2(x+5)=0`
`(3x-2)(x+5)=0`

Therefore
`x=2/3 or -5`