Solve 24x^2+20x

$$24 x ^ { 2 } + 20 x$$

Factor

$$4x\left(6x+5\right)$$

Solution Steps

Factor out 4.

$$4\left(6x^{2}+5x\right)$$

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

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

Rewrite the complete factored expression.

$$4x\left(6x+5\right)$$

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.

$$24x^{2}+20x=0$$

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.

$$x=\frac{-20±\sqrt{20^{2}}}{2\times 24}$$

Take the square root of 20^{2}.

$$x=\frac{-20±20}{2\times 24}$$

Multiply 2 times 24.

$$x=\frac{-20±20}{48}$$

Now solve the equation x=\frac{-20±20}{48} when ± is plus. Add -20 to 20.

$$x=\frac{0}{48}$$

Divide 0 by 48.

$$x=0$$

Now solve the equation x=\frac{-20±20}{48} when ± is minus. Subtract 20 from -20.

$$x=-\frac{40}{48}$$

Reduce the fraction \frac{-40}{48} to lowest terms by extracting and canceling out 8.

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

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}.

$$24x^{2}+20x=24x\left(x-\left(-\frac{5}{6}\right)\right)$$

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

$$24x^{2}+20x=24x\left(x+\frac{5}{6}\right)$$

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

$$24x^{2}+20x=24x\times \frac{6x+5}{6}$$

Cancel out 6, the greatest common factor in 24 and 6.

$$24x^{2}+20x=4x\left(6x+5\right)$$

Evaluate

$$4x\left(6x+5\right)$$