Solve (x+2)(x+4)+39=3(x+x+6)

$$( x + 2 ) ( x + 4 ) + 39 = 3 ( x + x + 6 )$$

Solve for x (complex solution)

$$x=-\sqrt{29}i\approx -0-5.385164807i$$

$$x=\sqrt{29}i\approx 5.385164807i$$

Steps by Finding Square Root

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

$$x^{2}+6x+8+39=3\left(x+x+6\right)$$

Add 8 and 39 to get 47.

$$x^{2}+6x+47=3\left(x+x+6\right)$$

Combine x and x to get 2x.

$$x^{2}+6x+47=3\left(2x+6\right)$$

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

$$x^{2}+6x+47=6x+18$$

Subtract 6x from both sides.

$$x^{2}+6x+47-6x=18$$

Combine 6x and -6x to get 0.

$$x^{2}+47=18$$

Subtract 47 from both sides.

$$x^{2}=18-47$$

Subtract 47 from 18 to get -29.

$$x^{2}=-29$$

The equation is now solved.

$$x=\sqrt{29}i x=-\sqrt{29}i$$

Steps Using the Quadratic Formula

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

$$x^{2}+6x+8+39=3\left(x+x+6\right)$$

Add 8 and 39 to get 47.

$$x^{2}+6x+47=3\left(x+x+6\right)$$

Combine x and x to get 2x.

$$x^{2}+6x+47=3\left(2x+6\right)$$

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

$$x^{2}+6x+47=6x+18$$

Subtract 6x from both sides.

$$x^{2}+6x+47-6x=18$$

Combine 6x and -6x to get 0.

$$x^{2}+47=18$$

Subtract 18 from both sides.

$$x^{2}+47-18=0$$

Subtract 18 from 47 to get 29.

$$x^{2}+29=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 29 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 29}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 29}}{2}$$

Multiply -4 times 29.

$$x=\frac{0±\sqrt{-116}}{2}$$

Take the square root of -116.

$$x=\frac{0±2\sqrt{29}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{29}i}{2} when ± is plus.

$$x=\sqrt{29}i$$

Now solve the equation x=\frac{0±2\sqrt{29}i}{2} when ± is minus.

$$x=-\sqrt{29}i$$

The equation is now solved.

$$x=\sqrt{29}i x=-\sqrt{29}i$$