Solve (3x^2+6x)

$$(3 { x }^{ 2 } +6x)$$

Factor

$$3x\left(x+2\right)$$

Solution Steps

Factor out 3.

$$3\left(x^{2}+2x\right)$$

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

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

Rewrite the complete factored expression.

$$3x\left(x+2\right)$$

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.

$$3x^{2}+6x=0$$

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.

$$x=\frac{-6±\sqrt{6^{2}}}{2\times 3}$$

Take the square root of 6^{2}.

$$x=\frac{-6±6}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{-6±6}{6}$$

Now solve the equation x=\frac{-6±6}{6} when ± is plus. Add -6 to 6.

$$x=\frac{0}{6}$$

Divide 0 by 6.

$$x=0$$

Now solve the equation x=\frac{-6±6}{6} when ± is minus. Subtract 6 from -6.

$$x=-\frac{12}{6}$$

Divide -12 by 6.

$$x=-2$$

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}.

$$3x^{2}+6x=3x\left(x-\left(-2\right)\right)$$

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

$$3x^{2}+6x=3x\left(x+2\right)$$

Evaluate

$$3x\left(x+2\right)$$