Solve 12p^2+10p

$$12 p ^ { 2 } + 10 p$$

Factor

$$2p\left(6p+5\right)$$

Solution Steps

Factor out 2.

$$2\left(6p^{2}+5p\right)$$

Consider 6p^{2}+5p. Factor out p.

$$p\left(6p+5\right)$$

Rewrite the complete factored expression.

$$2p\left(6p+5\right)$$

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.

$$12p^{2}+10p=0$$

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.

$$p=\frac{-10±\sqrt{10^{2}}}{2\times 12}$$

Take the square root of 10^{2}.

$$p=\frac{-10±10}{2\times 12}$$

Multiply 2 times 12.

$$p=\frac{-10±10}{24}$$

Now solve the equation p=\frac{-10±10}{24} when ± is plus. Add -10 to 10.

$$p=\frac{0}{24}$$

Divide 0 by 24.

$$p=0$$

Now solve the equation p=\frac{-10±10}{24} when ± is minus. Subtract 10 from -10.

$$p=-\frac{20}{24}$$

Reduce the fraction \frac{-20}{24} to lowest terms by extracting and canceling out 4.

$$p=-\frac{5}{6}$$

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{5}{6} for x_{2}.

$$12p^{2}+10p=12p\left(p-\left(-\frac{5}{6}\right)\right)$$

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

$$12p^{2}+10p=12p\left(p+\frac{5}{6}\right)$$

Add \frac{5}{6} to p by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$12p^{2}+10p=12p\times \frac{6p+5}{6}$$

Cancel out 6, the greatest common factor in 12 and 6.

$$12p^{2}+10p=2p\left(6p+5\right)$$

Evaluate

$$2p\left(6p+5\right)$$