Solve 6s^2+12s

$$6 s ^ { 2 } + 12 s$$

Factor

$$6s\left(s+2\right)$$

Solution Steps

Factor out 6.

$$6\left(s^{2}+2s\right)$$

Consider s^{2}+2s. Factor out s.

$$s\left(s+2\right)$$

Rewrite the complete factored expression.

$$6s\left(s+2\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$6s^{2}+12s=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$s=\frac{-12±\sqrt{12^{2}}}{2\times 6}$$

Take the square root of 12^{2}.

$$s=\frac{-12±12}{2\times 6}$$

Multiply 2 times 6.

$$s=\frac{-12±12}{12}$$

Now solve the equation s=\frac{-12±12}{12} when ± is plus. Add -12 to 12.

$$s=\frac{0}{12}$$

Divide 0 by 12.

$$s=0$$

Now solve the equation s=\frac{-12±12}{12} when ± is minus. Subtract 12 from -12.

$$s=-\frac{24}{12}$$

Divide -24 by 12.

$$s=-2$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 0 for x_{1} and -2 for x_{2}.

$$6s^{2}+12s=6s\left(s-\left(-2\right)\right)$$

Simplify all the expressions of the form p-\left(-q\right) to p+q.

$$6s^{2}+12s=6s\left(s+2\right)$$

Evaluate

$$6s\left(s+2\right)$$