Solve x(a^2-3)=2a^2-6a

$$x ( a ^ { 2 } - 3 ) = 2 a ^ { 2 } - 6 a$$

Factor

$$2a\left(a-3\right)$$

Solution Steps

Factor out 2.

$$2\left(a^{2}-3a\right)$$

Consider a^{2}-3a. Factor out a.

$$a\left(a-3\right)$$

Rewrite the complete factored expression.

$$2a\left(a-3\right)$$

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.

$$2a^{2}-6a=0$$

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.

$$a=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}}}{2\times 2}$$

Take the square root of \left(-6\right)^{2}.

$$a=\frac{-\left(-6\right)±6}{2\times 2}$$

The opposite of -6 is 6.

$$a=\frac{6±6}{2\times 2}$$

Multiply 2 times 2.

$$a=\frac{6±6}{4}$$

Now solve the equation a=\frac{6±6}{4} when ± is plus. Add 6 to 6.

$$a=\frac{12}{4}$$

Divide 12 by 4.

$$a=3$$

Now solve the equation a=\frac{6±6}{4} when ± is minus. Subtract 6 from 6.

$$a=\frac{0}{4}$$

Divide 0 by 4.

$$a=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 3 for x_{1} and 0 for x_{2}.

$$2a^{2}-6a=2\left(a-3\right)a$$

Evaluate

$$2a\left(a-3\right)$$