Solve (5x+3)(2x-4)=12

$$(5x+3)(2x-4)=12$$

Solve for x

$$x=-1$$

$$x = \frac{12}{5} = 2\frac{2}{5} = 2.4$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 5x+3 by 2x-4 and combine like terms.

$$10x^{2}-14x-12=12$$

Subtract 12 from both sides.

$$10x^{2}-14x-12-12=0$$

Subtract 12 from -12 to get -24.

$$10x^{2}-14x-24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, -14 for b, and -24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}-4\times 10\left(-24\right)}}{2\times 10}$$

Square -14.

$$x=\frac{-\left(-14\right)±\sqrt{196-4\times 10\left(-24\right)}}{2\times 10}$$

Multiply -4 times 10.

$$x=\frac{-\left(-14\right)±\sqrt{196-40\left(-24\right)}}{2\times 10}$$

Multiply -40 times -24.

$$x=\frac{-\left(-14\right)±\sqrt{196+960}}{2\times 10}$$

Add 196 to 960.

$$x=\frac{-\left(-14\right)±\sqrt{1156}}{2\times 10}$$

Take the square root of 1156.

$$x=\frac{-\left(-14\right)±34}{2\times 10}$$

The opposite of -14 is 14.

$$x=\frac{14±34}{2\times 10}$$

Multiply 2 times 10.

$$x=\frac{14±34}{20}$$

Now solve the equation x=\frac{14±34}{20} when ± is plus. Add 14 to 34.

$$x=\frac{48}{20}$$

Reduce the fraction \frac{48}{20} to lowest terms by extracting and canceling out 4.

$$x=\frac{12}{5}$$

Now solve the equation x=\frac{14±34}{20} when ± is minus. Subtract 34 from 14.

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

Divide -20 by 20.

$$x=-1$$

The equation is now solved.

$$x=\frac{12}{5} x=-1$$

Steps for Completing the Square

Use the distributive property to multiply 5x+3 by 2x-4 and combine like terms.

$$10x^{2}-14x-12=12$$

Add 12 to both sides.

$$10x^{2}-14x=12+12$$

Add 12 and 12 to get 24.

$$10x^{2}-14x=24$$

Divide both sides by 10.

$$\frac{10x^{2}-14x}{10}=\frac{24}{10}$$

Dividing by 10 undoes the multiplication by 10.

$$x^{2}+\left(-\frac{14}{10}\right)x=\frac{24}{10}$$

Reduce the fraction \frac{-14}{10} to lowest terms by extracting and canceling out 2.

$$x^{2}-\frac{7}{5}x=\frac{24}{10}$$

Reduce the fraction \frac{24}{10} to lowest terms by extracting and canceling out 2.

$$x^{2}-\frac{7}{5}x=\frac{12}{5}$$

Divide -\frac{7}{5}, the coefficient of the x term, by 2 to get -\frac{7}{10}. Then add the square of -\frac{7}{10} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{7}{5}x+\left(-\frac{7}{10}\right)^{2}=\frac{12}{5}+\left(-\frac{7}{10}\right)^{2}$$

Square -\frac{7}{10} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{7}{5}x+\frac{49}{100}=\frac{12}{5}+\frac{49}{100}$$

Add \frac{12}{5} to \frac{49}{100} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-\frac{7}{5}x+\frac{49}{100}=\frac{289}{100}$$

Factor x^{2}-\frac{7}{5}x+\frac{49}{100}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{7}{10}\right)^{2}=\frac{289}{100}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{7}{10}\right)^{2}}=\sqrt{\frac{289}{100}}$$

Simplify.

$$x-\frac{7}{10}=\frac{17}{10} x-\frac{7}{10}=-\frac{17}{10}$$

Add \frac{7}{10} to both sides of the equation.

$$x=\frac{12}{5} x=-1$$