Question 232489
Because of the {{{x^2}}} term, this is a quadratic equation. To solve quadratic equations<ol><li>Simplify each side</li><li>Get one side equal to zero by adding or subtracting appropriate terms.</li><li>Use the quadratic formula or factor</li><li>If you factored in the previous step, use the Zero Product Property and solve.</li></ol>
Let's try this on your equation.
{{{3x^2-12x=63}}}
1. Simplify.
Your equation is already simplified.
2. Get one side equal to zero.
Subtract 63 from each side:
{{{3x^2-12x-63=0}}}
3. Factor or use the quadratic formula. (I prefer factoring when it can be done so we'll factor.)
Always start factoring with the Greatest Common Factor (GCF). Here the GCF is 3:
{{{3(x^2-4x-21) = 0}}}
Always keep factoring until you can factor no more. The trinomial will factor:
{{{3(x-7)(x+3) = 0}}}
4. Use the Zero Product Property. This property says that the only way a product can be zero is if one of the factors is zero. So our solutions will be x values that make one of the factors zero. 3 cannot be a zero. But the other two, with x in them, could be:
{{{x-7 = 0}}} or {{{ x+3 = 0}}}
Solving these we get:
{{{x = 7}}} or {{{x = -3}}}