Solve 10x-12x^2=

$$10x-12 { x }^{ 2 } =$$

Factor

$$2x\left(5-6x\right)$$

Solution Steps

Factor out 2.

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

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

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

Rewrite the complete factored expression.

$$2x\left(-6x+5\right)$$

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.

$$-12x^{2}+10x=0$$

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.

$$x=\frac{-10±\sqrt{10^{2}}}{2\left(-12\right)}$$

Take the square root of 10^{2}.

$$x=\frac{-10±10}{2\left(-12\right)}$$

Multiply 2 times -12.

$$x=\frac{-10±10}{-24}$$

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

$$x=\frac{0}{-24}$$

Divide 0 by -24.

$$x=0$$

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

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

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

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

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}.

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

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

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

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

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

Evaluate

$$2x\left(5-6x\right)$$