4( x-3)-10=-5x(x+6)

To solve the equation 4(x - 3) - 10 = -5x(x + 6), we can follow these steps:

1. Distribute the 4 and -5x across the parentheses: 4x - 12 - 10 = -5x^2 - 30x

2. Combine like terms on both sides of the equation: 4x - 22 = -5x^2 - 30x

3. Move all terms to one side to obtain a quadratic equation: -5x^2 - 30x - 4x + 22 = 0

4. Simplify: -5x^2 - 34x + 22 = 0

5. To solve the quadratic equation, we can either factor it or use the quadratic formula. Let's use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

   In our case, a = -5, b = -34, and c = 22.

   x = (-(-34) ± √((-34)^2 - 4(-5)(22))) / (2(-5)) x = (34 ± √(1156 + 440)) / (-10) x = (34 ± √1596) / (-10) x = (34 ± 39.95) / (-10)

6. Solve for x: x = (34 + 39.95) / (-10) or x = (34 - 39.95) / (-10) x = 73.95 / (-10) or x = -5.95 / (-10) x = -7.395 or x = 0.595

Therefore, the solutions to the equation 4(x - 3) - 10 = -5x(x + 6) are x = -7.395 and x = 0.595.