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

$$2 x ( 3 x - 6 ) = 3 ( 3 x - 6 )$$

Solve for x

$$x=2$$

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2x by 3x-6.

$$6x^{2}-12x=3\left(3x-6\right)$$

Use the distributive property to multiply 3 by 3x-6.

$$6x^{2}-12x=9x-18$$

Subtract 9x from both sides.

$$6x^{2}-12x-9x=-18$$

Combine -12x and -9x to get -21x.

$$6x^{2}-21x=-18$$

Add 18 to both sides.

$$6x^{2}-21x+18=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, -21 for b, and 18 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-21\right)±\sqrt{\left(-21\right)^{2}-4\times 6\times 18}}{2\times 6}$$

Square -21.

$$x=\frac{-\left(-21\right)±\sqrt{441-4\times 6\times 18}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{-\left(-21\right)±\sqrt{441-24\times 18}}{2\times 6}$$

Multiply -24 times 18.

$$x=\frac{-\left(-21\right)±\sqrt{441-432}}{2\times 6}$$

Add 441 to -432.

$$x=\frac{-\left(-21\right)±\sqrt{9}}{2\times 6}$$

Take the square root of 9.

$$x=\frac{-\left(-21\right)±3}{2\times 6}$$

The opposite of -21 is 21.

$$x=\frac{21±3}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{21±3}{12}$$

Now solve the equation x=\frac{21±3}{12} when ± is plus. Add 21 to 3.

$$x=\frac{24}{12}$$

Divide 24 by 12.

$$x=2$$

Now solve the equation x=\frac{21±3}{12} when ± is minus. Subtract 3 from 21.

$$x=\frac{18}{12}$$

Reduce the fraction \frac{18}{12} to lowest terms by extracting and canceling out 6.

$$x=\frac{3}{2}$$

The equation is now solved.

$$x=2 x=\frac{3}{2}$$

Steps for Completing the Square

Use the distributive property to multiply 2x by 3x-6.

$$6x^{2}-12x=3\left(3x-6\right)$$

Use the distributive property to multiply 3 by 3x-6.

$$6x^{2}-12x=9x-18$$

Subtract 9x from both sides.

$$6x^{2}-12x-9x=-18$$

Combine -12x and -9x to get -21x.

$$6x^{2}-21x=-18$$

Divide both sides by 6.

$$\frac{6x^{2}-21x}{6}=-\frac{18}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$x^{2}+\left(-\frac{21}{6}\right)x=-\frac{18}{6}$$

Reduce the fraction \frac{-21}{6} to lowest terms by extracting and canceling out 3.

$$x^{2}-\frac{7}{2}x=-\frac{18}{6}$$

Divide -18 by 6.

$$x^{2}-\frac{7}{2}x=-3$$

Divide -\frac{7}{2}, the coefficient of the x term, by 2 to get -\frac{7}{4}. Then add the square of -\frac{7}{4} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{7}{2}x+\left(-\frac{7}{4}\right)^{2}=-3+\left(-\frac{7}{4}\right)^{2}$$

Square -\frac{7}{4} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{7}{2}x+\frac{49}{16}=-3+\frac{49}{16}$$

Add -3 to \frac{49}{16}.

$$x^{2}-\frac{7}{2}x+\frac{49}{16}=\frac{1}{16}$$

Factor x^{2}-\frac{7}{2}x+\frac{49}{16}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{7}{4}\right)^{2}=\frac{1}{16}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{7}{4}\right)^{2}}=\sqrt{\frac{1}{16}}$$

Simplify.

$$x-\frac{7}{4}=\frac{1}{4} x-\frac{7}{4}=-\frac{1}{4}$$

Add \frac{7}{4} to both sides of the equation.

$$x=2 x=\frac{3}{2}$$