Solve (4x+5)*(3x-1/6)=3

$$( 4 x + 5 ) \cdot ( \frac { 3 x - 1 } { 6 } ) = 3$$

Solve for x

$$x = -\frac{23}{12} = -1\frac{11}{12} \approx -1.916666667$$

$$x=1$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 6.

$$\left(4x+5\right)\left(3x-1\right)=18$$

Apply the distributive property by multiplying each term of 4x+5 by each term of 3x-1.

$$12x^{2}-4x+15x-5=18$$

Combine -4x and 15x to get 11x.

$$12x^{2}+11x-5=18$$

Subtract 18 from both sides.

$$12x^{2}+11x-5-18=0$$

Subtract 18 from -5 to get -23.

$$12x^{2}+11x-23=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 12 for a, 11 for b, and -23 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-11±\sqrt{11^{2}-4\times 12\left(-23\right)}}{2\times 12}$$

Square 11.

$$x=\frac{-11±\sqrt{121-4\times 12\left(-23\right)}}{2\times 12}$$

Multiply -4 times 12.

$$x=\frac{-11±\sqrt{121-48\left(-23\right)}}{2\times 12}$$

Multiply -48 times -23.

$$x=\frac{-11±\sqrt{121+1104}}{2\times 12}$$

Add 121 to 1104.

$$x=\frac{-11±\sqrt{1225}}{2\times 12}$$

Take the square root of 1225.

$$x=\frac{-11±35}{2\times 12}$$

Multiply 2 times 12.

$$x=\frac{-11±35}{24}$$

Now solve the equation x=\frac{-11±35}{24} when ± is plus. Add -11 to 35.

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

Divide 24 by 24.

$$x=1$$

Now solve the equation x=\frac{-11±35}{24} when ± is minus. Subtract 35 from -11.

$$x=-\frac{46}{24}$$

Reduce the fraction \frac{-46}{24} to lowest terms by extracting and canceling out 2.

$$x=-\frac{23}{12}$$

The equation is now solved.

$$x=1 x=-\frac{23}{12}$$

Steps for Completing the Square

Multiply both sides of the equation by 6.

$$\left(4x+5\right)\left(3x-1\right)=18$$

Apply the distributive property by multiplying each term of 4x+5 by each term of 3x-1.

$$12x^{2}-4x+15x-5=18$$

Combine -4x and 15x to get 11x.

$$12x^{2}+11x-5=18$$

Add 5 to both sides.

$$12x^{2}+11x=18+5$$

Add 18 and 5 to get 23.

$$12x^{2}+11x=23$$

Divide both sides by 12.

$$\frac{12x^{2}+11x}{12}=\frac{23}{12}$$

Dividing by 12 undoes the multiplication by 12.

$$x^{2}+\frac{11}{12}x=\frac{23}{12}$$

Divide \frac{11}{12}, the coefficient of the x term, by 2 to get \frac{11}{24}. Then add the square of \frac{11}{24} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{11}{12}x+\left(\frac{11}{24}\right)^{2}=\frac{23}{12}+\left(\frac{11}{24}\right)^{2}$$

Square \frac{11}{24} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{11}{12}x+\frac{121}{576}=\frac{23}{12}+\frac{121}{576}$$

Add \frac{23}{12} to \frac{121}{576} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{11}{12}x+\frac{121}{576}=\frac{1225}{576}$$

Factor x^{2}+\frac{11}{12}x+\frac{121}{576}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{11}{24}\right)^{2}=\frac{1225}{576}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{11}{24}\right)^{2}}=\sqrt{\frac{1225}{576}}$$

Simplify.

$$x+\frac{11}{24}=\frac{35}{24} x+\frac{11}{24}=-\frac{35}{24}$$

Subtract \frac{11}{24} from both sides of the equation.

$$x=1 x=-\frac{23}{12}$$