Solve 30d-25d^2

$$30 d - 25 d ^ { 2 }$$

Factor

$$5d\left(6-5d\right)$$

Solution Steps

Factor out 5.

$$5\left(6d-5d^{2}\right)$$

Consider 6d-5d^{2}. Factor out d.

$$d\left(6-5d\right)$$

Rewrite the complete factored expression.

$$5d\left(-5d+6\right)$$

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.

$$-25d^{2}+30d=0$$

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.

$$d=\frac{-30±\sqrt{30^{2}}}{2\left(-25\right)}$$

Take the square root of 30^{2}.

$$d=\frac{-30±30}{2\left(-25\right)}$$

Multiply 2 times -25.

$$d=\frac{-30±30}{-50}$$

Now solve the equation d=\frac{-30±30}{-50} when ± is plus. Add -30 to 30.

$$d=\frac{0}{-50}$$

Divide 0 by -50.

$$d=0$$

Now solve the equation d=\frac{-30±30}{-50} when ± is minus. Subtract 30 from -30.

$$d=-\frac{60}{-50}$$

Reduce the fraction \frac{-60}{-50} to lowest terms by extracting and canceling out 10.

$$d=\frac{6}{5}$$

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

$$-25d^{2}+30d=-25d\left(d-\frac{6}{5}\right)$$

Subtract \frac{6}{5} from d by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$-25d^{2}+30d=-25d\times \frac{-5d+6}{-5}$$

Cancel out 5, the greatest common factor in -25 and -5.

$$-25d^{2}+30d=5d\left(-5d+6\right)$$

Evaluate

$$5d\left(6-5d\right)$$