1) (x+2)(x-3) - (2x-5)(x+3) = x(x-5)Expanding each term, we have:(x^2 - 3x + 2x - 6) - (2x^2 + 6x - 5x - 15) = x^2 - 5xNow simplify the equation:x^2 - x - 6 - 2x^2 + x + 15 = x^2 - 5x-x^2 + 10 = x^2 - 5xCombine like terms:10 = 2x^2 - 5xRearrange the equation:2x^2 - 5x - 10 = 0
2) (6x-5)^2 + (3x-2)(3x+2) = 36Expanding the terms:(6x-5)(6x-5) + (9x^2 - 4) = 36Simplify:36x^2 - 30x - 30 + 9x^2 - 4 = 36Combine like terms:45x^2 - 30x - 34 = 36Rearrange the equation:45x^2 - 30x - 34 - 36 = 045x^2 - 30x - 70 = 0
1) (x+2)(x-3) - (2x-5)(x+3) = x(x-5)
Expanding each term, we have:
(x^2 - 3x + 2x - 6) - (2x^2 + 6x - 5x - 15) = x^2 - 5x
Now simplify the equation:
x^2 - x - 6 - 2x^2 + x + 15 = x^2 - 5x
-x^2 + 10 = x^2 - 5x
Combine like terms:
10 = 2x^2 - 5x
Rearrange the equation:
2x^2 - 5x - 10 = 0
2) (6x-5)^2 + (3x-2)(3x+2) = 36
Expanding the terms:
(6x-5)(6x-5) + (9x^2 - 4) = 36
Simplify:
36x^2 - 30x - 30 + 9x^2 - 4 = 36
Combine like terms:
45x^2 - 30x - 34 = 36
Rearrange the equation:
45x^2 - 30x - 34 - 36 = 0
45x^2 - 30x - 70 = 0