(2x-6)(8x+5)+(3-4x)(3+4x)=55

Jasonbradley

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Jun 16, 2024

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Solving the Equation: (2x-6)(8x+5)+(3-4x)(3+4x)=55

This article will guide you through the process of solving the equation (2x-6)(8x+5)+(3-4x)(3+4x)=55. We will break down the steps and explain the concepts used.

Expanding the Equation

First, we need to expand the equation by multiplying the expressions in parentheses. We can use the FOIL method (First, Outer, Inner, Last) for this.

Step 1: Expand the first set of parentheses:

(2x-6)(8x+5) = (2x * 8x) + (2x * 5) + (-6 * 8x) + (-6 * 5) = 16x² + 10x - 48x - 30

Step 2: Expand the second set of parentheses:

(3-4x)(3+4x) = (3 * 3) + (3 * 4x) + (-4x * 3) + (-4x * 4x) = 9 + 12x - 12x - 16x²

Step 3: Simplify the equation:

Now, we can substitute the expanded expressions back into the original equation and combine like terms:

16x² + 10x - 48x - 30 + 9 + 12x - 12x - 16x² = 55

Step 4: Combine like terms:

-18x - 21 = 55

Solving for x

Now we have a simplified linear equation. We can solve for 'x' using the following steps:

Step 1: Isolate the 'x' term:

Add 21 to both sides of the equation:

-18x = 76

Step 2: Solve for 'x':

Divide both sides by -18:

x = -76/18

Step 3: Simplify the solution:

Simplify the fraction:

x = -38/9

Therefore, the solution to the equation (2x-6)(8x+5)+(3-4x)(3+4x)=55 is x = -38/9.