Solve -24x^2+18x

$$- 24 x ^ { 2 } + 18 x$$

Factor

$$6x\left(3-4x\right)$$

Solution Steps

Factor out 6.

$$6\left(-4x^{2}+3x\right)$$

Consider -4x^{2}+3x. Factor out x.

$$x\left(-4x+3\right)$$

Rewrite the complete factored expression.

$$6x\left(-4x+3\right)$$

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.

$$-24x^{2}+18x=0$$

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.

$$x=\frac{-18±\sqrt{18^{2}}}{2\left(-24\right)}$$

Take the square root of 18^{2}.

$$x=\frac{-18±18}{2\left(-24\right)}$$

Multiply 2 times -24.

$$x=\frac{-18±18}{-48}$$

Now solve the equation x=\frac{-18±18}{-48} when ± is plus. Add -18 to 18.

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

Divide 0 by -48.

$$x=0$$

Now solve the equation x=\frac{-18±18}{-48} when ± is minus. Subtract 18 from -18.

$$x=-\frac{36}{-48}$$

Reduce the fraction \frac{-36}{-48} to lowest terms by extracting and canceling out 12.

$$x=\frac{3}{4}$$

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}{4} for x_{2}.

$$-24x^{2}+18x=-24x\left(x-\frac{3}{4}\right)$$

Subtract \frac{3}{4} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$-24x^{2}+18x=-24x\times \frac{-4x+3}{-4}$$

Cancel out 4, the greatest common factor in -24 and -4.

$$-24x^{2}+18x=6x\left(-4x+3\right)$$

Evaluate

$$6x\left(3-4x\right)$$