Solve 3(2x+3)6x=4x-4

$$3(2x+3)6x=4x-4$$

Solve for x

$$x=\frac{\sqrt{481}-25}{36}\approx -0.085230217$$

$$x=\frac{-\sqrt{481}-25}{36}\approx -1.303658672$$

Steps Using the Quadratic Formula

Multiply 3 and 6 to get 18.

$$18\left(2x+3\right)x=4x-4$$

Use the distributive property to multiply 18 by 2x+3.

$$\left(36x+54\right)x=4x-4$$

Use the distributive property to multiply 36x+54 by x.

$$36x^{2}+54x=4x-4$$

Subtract 4x from both sides.

$$36x^{2}+54x-4x=-4$$

Combine 54x and -4x to get 50x.

$$36x^{2}+50x=-4$$

Add 4 to both sides.

$$36x^{2}+50x+4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 36 for a, 50 for b, and 4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-50±\sqrt{50^{2}-4\times 36\times 4}}{2\times 36}$$

Square 50.

$$x=\frac{-50±\sqrt{2500-4\times 36\times 4}}{2\times 36}$$

Multiply -4 times 36.

$$x=\frac{-50±\sqrt{2500-144\times 4}}{2\times 36}$$

Multiply -144 times 4.

$$x=\frac{-50±\sqrt{2500-576}}{2\times 36}$$

Add 2500 to -576.

$$x=\frac{-50±\sqrt{1924}}{2\times 36}$$

Take the square root of 1924.

$$x=\frac{-50±2\sqrt{481}}{2\times 36}$$

Multiply 2 times 36.

$$x=\frac{-50±2\sqrt{481}}{72}$$

Now solve the equation x=\frac{-50±2\sqrt{481}}{72} when ± is plus. Add -50 to 2\sqrt{481}.

$$x=\frac{2\sqrt{481}-50}{72}$$

Divide -50+2\sqrt{481} by 72.

$$x=\frac{\sqrt{481}-25}{36}$$

Now solve the equation x=\frac{-50±2\sqrt{481}}{72} when ± is minus. Subtract 2\sqrt{481} from -50.

$$x=\frac{-2\sqrt{481}-50}{72}$$

Divide -50-2\sqrt{481} by 72.

$$x=\frac{-\sqrt{481}-25}{36}$$

The equation is now solved.

$$x=\frac{\sqrt{481}-25}{36} x=\frac{-\sqrt{481}-25}{36}$$

Steps for Completing the Square

Multiply 3 and 6 to get 18.

$$18\left(2x+3\right)x=4x-4$$

Use the distributive property to multiply 18 by 2x+3.

$$\left(36x+54\right)x=4x-4$$

Use the distributive property to multiply 36x+54 by x.

$$36x^{2}+54x=4x-4$$

Subtract 4x from both sides.

$$36x^{2}+54x-4x=-4$$

Combine 54x and -4x to get 50x.

$$36x^{2}+50x=-4$$

Divide both sides by 36.

$$\frac{36x^{2}+50x}{36}=-\frac{4}{36}$$

Dividing by 36 undoes the multiplication by 36.

$$x^{2}+\frac{50}{36}x=-\frac{4}{36}$$

Reduce the fraction \frac{50}{36} to lowest terms by extracting and canceling out 2.

$$x^{2}+\frac{25}{18}x=-\frac{4}{36}$$

Reduce the fraction \frac{-4}{36} to lowest terms by extracting and canceling out 4.

$$x^{2}+\frac{25}{18}x=-\frac{1}{9}$$

Divide \frac{25}{18}, the coefficient of the x term, by 2 to get \frac{25}{36}. Then add the square of \frac{25}{36} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{25}{18}x+\left(\frac{25}{36}\right)^{2}=-\frac{1}{9}+\left(\frac{25}{36}\right)^{2}$$

Square \frac{25}{36} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{25}{18}x+\frac{625}{1296}=-\frac{1}{9}+\frac{625}{1296}$$

Add -\frac{1}{9} to \frac{625}{1296} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{25}{18}x+\frac{625}{1296}=\frac{481}{1296}$$

Factor x^{2}+\frac{25}{18}x+\frac{625}{1296}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{25}{36}\right)^{2}=\frac{481}{1296}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{25}{36}\right)^{2}}=\sqrt{\frac{481}{1296}}$$

Simplify.

$$x+\frac{25}{36}=\frac{\sqrt{481}}{36} x+\frac{25}{36}=-\frac{\sqrt{481}}{36}$$

Subtract \frac{25}{36} from both sides of the equation.

$$x=\frac{\sqrt{481}-25}{36} x=\frac{-\sqrt{481}-25}{36}$$