Solve 42c^2+24c

$$42 c ^ { 2 } + 24 c$$

Factor

$$6c\left(7c+4\right)$$

Solution Steps

Factor out 6.

$$6\left(7c^{2}+4c\right)$$

Consider 7c^{2}+4c. Factor out c.

$$c\left(7c+4\right)$$

Rewrite the complete factored expression.

$$6c\left(7c+4\right)$$

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.

$$42c^{2}+24c=0$$

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.

$$c=\frac{-24±\sqrt{24^{2}}}{2\times 42}$$

Take the square root of 24^{2}.

$$c=\frac{-24±24}{2\times 42}$$

Multiply 2 times 42.

$$c=\frac{-24±24}{84}$$

Now solve the equation c=\frac{-24±24}{84} when ± is plus. Add -24 to 24.

$$c=\frac{0}{84}$$

Divide 0 by 84.

$$c=0$$

Now solve the equation c=\frac{-24±24}{84} when ± is minus. Subtract 24 from -24.

$$c=-\frac{48}{84}$$

Reduce the fraction \frac{-48}{84} to lowest terms by extracting and canceling out 12.

$$c=-\frac{4}{7}$$

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 -\frac{4}{7} for x_{2}.

$$42c^{2}+24c=42c\left(c-\left(-\frac{4}{7}\right)\right)$$

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

$$42c^{2}+24c=42c\left(c+\frac{4}{7}\right)$$

Add \frac{4}{7} to c by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$42c^{2}+24c=42c\times \frac{7c+4}{7}$$

Cancel out 7, the greatest common factor in 42 and 7.

$$42c^{2}+24c=6c\left(7c+4\right)$$

Evaluate

$$6c\left(7c+4\right)$$