Solve 5z^2+3z

$$5 z ^ { 2 } + 3 z$$

Factor

$$z\left(5z+3\right)$$

Solution Steps

Factor out z.

$$z\left(5z+3\right)$$

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.

$$5z^{2}+3z=0$$

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.

$$z=\frac{-3±\sqrt{3^{2}}}{2\times 5}$$

Take the square root of 3^{2}.

$$z=\frac{-3±3}{2\times 5}$$

Multiply 2 times 5.

$$z=\frac{-3±3}{10}$$

Now solve the equation z=\frac{-3±3}{10} when ± is plus. Add -3 to 3.

$$z=\frac{0}{10}$$

Divide 0 by 10.

$$z=0$$

Now solve the equation z=\frac{-3±3}{10} when ± is minus. Subtract 3 from -3.

$$z=-\frac{6}{10}$$

Reduce the fraction \frac{-6}{10} to lowest terms by extracting and canceling out 2.

$$z=-\frac{3}{5}$$

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{3}{5} for x_{2}.

$$5z^{2}+3z=5z\left(z-\left(-\frac{3}{5}\right)\right)$$

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

$$5z^{2}+3z=5z\left(z+\frac{3}{5}\right)$$

Add \frac{3}{5} to z by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$5z^{2}+3z=5z\times \frac{5z+3}{5}$$

Cancel out 5, the greatest common factor in 5 and 5.

$$5z^{2}+3z=z\left(5z+3\right)$$

Evaluate

$$z\left(5z+3\right)$$