(3 + 5x) (2 – 3x) = 12 – 15x2

Jasonbradley

2 min read

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Jun 16, 2024

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Expanding and Solving the Equation: (3 + 5x)(2 – 3x) = 12 – 15x²

This article will walk through the process of expanding and solving the equation (3 + 5x)(2 – 3x) = 12 – 15x². We will use the FOIL method to expand the left side of the equation and then simplify to find the solution.

Expanding the Left Side

The FOIL method stands for First, Outer, Inner, Last. It's a mnemonic device to help remember how to multiply two binomials:

1. First: Multiply the first terms of each binomial: 3 * 2 = 6
2. Outer: Multiply the outer terms of the binomials: 3 * -3x = -9x
3. Inner: Multiply the inner terms of the binomials: 5x * 2 = 10x
4. Last: Multiply the last terms of the binomials: 5x * -3x = -15x²

Therefore, the expanded left side of the equation becomes: 6 - 9x + 10x - 15x²

Simplifying the Equation

Now, let's combine the like terms:

6 - 9x + 10x - 15x² = 12 - 15x²

This simplifies to:

x + 6 = 12

Solving for x

Finally, we can solve for x:

• Subtract 6 from both sides: x = 6

Therefore, the solution to the equation (3 + 5x)(2 – 3x) = 12 – 15x² is x = 6.