Solve 3x(x+5)=5(x+5)

$$3x(x+5)=5(x+5)$$

Solve for x

$$x=-5$$

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 3x by x+5.

$$3x^{2}+15x=5\left(x+5\right)$$

Use the distributive property to multiply 5 by x+5.

$$3x^{2}+15x=5x+25$$

Subtract 5x from both sides.

$$3x^{2}+15x-5x=25$$

Combine 15x and -5x to get 10x.

$$3x^{2}+10x=25$$

Subtract 25 from both sides.

$$3x^{2}+10x-25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 10 for b, and -25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-10±\sqrt{10^{2}-4\times 3\left(-25\right)}}{2\times 3}$$

Square 10.

$$x=\frac{-10±\sqrt{100-4\times 3\left(-25\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{-10±\sqrt{100-12\left(-25\right)}}{2\times 3}$$

Multiply -12 times -25.

$$x=\frac{-10±\sqrt{100+300}}{2\times 3}$$

Add 100 to 300.

$$x=\frac{-10±\sqrt{400}}{2\times 3}$$

Take the square root of 400.

$$x=\frac{-10±20}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{-10±20}{6}$$

Now solve the equation x=\frac{-10±20}{6} when ± is plus. Add -10 to 20.

$$x=\frac{10}{6}$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

$$x=\frac{5}{3}$$

Now solve the equation x=\frac{-10±20}{6} when ± is minus. Subtract 20 from -10.

$$x=-\frac{30}{6}$$

Divide -30 by 6.

$$x=-5$$

The equation is now solved.

$$x=\frac{5}{3} x=-5$$

Steps for Completing the Square

Use the distributive property to multiply 3x by x+5.

$$3x^{2}+15x=5\left(x+5\right)$$

Use the distributive property to multiply 5 by x+5.

$$3x^{2}+15x=5x+25$$

Subtract 5x from both sides.

$$3x^{2}+15x-5x=25$$

Combine 15x and -5x to get 10x.

$$3x^{2}+10x=25$$

Divide both sides by 3.

$$\frac{3x^{2}+10x}{3}=\frac{25}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x^{2}+\frac{10}{3}x=\frac{25}{3}$$

Divide \frac{10}{3}, the coefficient of the x term, by 2 to get \frac{5}{3}. Then add the square of \frac{5}{3} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{10}{3}x+\left(\frac{5}{3}\right)^{2}=\frac{25}{3}+\left(\frac{5}{3}\right)^{2}$$

Square \frac{5}{3} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{10}{3}x+\frac{25}{9}=\frac{25}{3}+\frac{25}{9}$$

Add \frac{25}{3} to \frac{25}{9} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{10}{3}x+\frac{25}{9}=\frac{100}{9}$$

Factor x^{2}+\frac{10}{3}x+\frac{25}{9}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{5}{3}\right)^{2}=\frac{100}{9}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{5}{3}\right)^{2}}=\sqrt{\frac{100}{9}}$$

Simplify.

$$x+\frac{5}{3}=\frac{10}{3} x+\frac{5}{3}=-\frac{10}{3}$$

Subtract \frac{5}{3} from both sides of the equation.

$$x=\frac{5}{3} x=-5$$