What do I do first in this problem? 4x(6x+6)=38

Question

It's a distributive problem and I don't know what to do first. Please help me

Answer 1

4x(6x+6)=38

Step 1: Distribute 24x² + 24x = 38

Step 2: Get rid of coefficient in front of x², so factoring is easier.

                              x² + x = ³⁸/₂₄

Step 3: Reduce the fraction on the right side.

                             x² + x = ¹⁹/₁₂

Step 4: Complete the square on the left side.

                            x² + x + ¹/₄ = ¹⁹/₁₂ + ¹/₄

Step 5: factor the equation on the left and reduce the numerical expression on the right.

                           (x + ¹/₂)² = ²²/₁₂

Step 6: In order to solve for x, take the square root of the number on the right side. 

                          (x + ¹/₂) = (plus or minus) sqrt (²²/₁₂)

Step 7: x = ¹/₆ (-3 - sqrt(66))

            x = ¹/₆ (sqrt(66) - 3)

Answer 2

First you have to distribute the 6x to the 4x+4 to get.

24x^2+24x=38

Since there are no easy factors, we'll need to proceed with the completing square method.

First divide both sides by 24

x^2+x=38/24

Then complete the square on left

(x+1/2)^2 - 1/4 = 38/24

(x+1/2)^2 = 44/24

x+1/2 = +- 44/24

x = -1/2 +- 11/6