Answer: x = 1, 15
Explanation:
It is given that these triangles are similar, which means their corresponding side lengths will be proportional. Using this information, we can set up a proportion.
Next, we can cross-multiply. We will foil the left side and distribute the 3x in the right side.
(2x - 3) * (x + 5) = (3x) * (x - 3)
2x² + 7x - 15 = 3x² - 9x
Now, we will solve the x-variable. To do this, we will subtract (3x² - 9x) from both sides of the equation.
2x² - 3x² + 7x + 9x - 15 = 0
Combine like terms.
-x² + 16x - 15 = 0
Factor out a -1. Then, divide both sides of the equation by -1.
-1(x² - 16x + 15) = 0
x² - 16x + 15 = 0
Factor into two two-term polynomials.
x² - 16x + 15 = 0
(x - 1)(x + 15) = 0
Solve with the zero product property.
x = 1, 15