Solve 6x^2+42x

$$6 x ^ { 2 } + 42 x$$

Factor

$$6x\left(x+7\right)$$

Solution Steps

Factor out 6.

$$6\left(x^{2}+7x\right)$$

Consider x^{2}+7x. Factor out x.

$$x\left(x+7\right)$$

Rewrite the complete factored expression.

$$6x\left(x+7\right)$$

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.

$$6x^{2}+42x=0$$

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.

$$x=\frac{-42±\sqrt{42^{2}}}{2\times 6}$$

Take the square root of 42^{2}.

$$x=\frac{-42±42}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{-42±42}{12}$$

Now solve the equation x=\frac{-42±42}{12} when ± is plus. Add -42 to 42.

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

Divide 0 by 12.

$$x=0$$

Now solve the equation x=\frac{-42±42}{12} when ± is minus. Subtract 42 from -42.

$$x=-\frac{84}{12}$$

Divide -84 by 12.

$$x=-7$$

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 -7 for x_{2}.

$$6x^{2}+42x=6x\left(x-\left(-7\right)\right)$$

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

$$6x^{2}+42x=6x\left(x+7\right)$$

Evaluate

$$6x\left(x+7\right)$$