1) x(x+3) = 10
Expanding the left side:
x^2 + 3x = 10
Subtracting 10 from both sides:
x^2 + 3x - 10 = 0
Factoring the quadratic equation:
(x + 5)(x - 2) = 0
Setting each factor to zero:
x + 5 = 0 or x - 2 = 0
x = -5 or x = 2

2) x(x-1) = 42
Expanding the left side:
x^2 - x = 42
Subtracting 42 from both sides:
x^2 - x - 42 = 0
Factoring the quadratic equation:
(x - 7)(x + 6) = 0
Setting each factor to zero:
x - 7 = 0 or x + 6 = 0
x = 7 or x = -6

3) (x+7)x = 18
Expanding the left side:
x^2 + 7x = 18
Subtracting 18 from both sides:
x^2 + 7x - 18 = 0
Factoring the quadratic equation:
(x + 9)(x - 2) = 0
Setting each factor to zero:
x + 9 = 0 or x - 2 = 0
x = -9 or x = 2

4) (x-9)x = 36
Expanding the left side:
x^2 - 9x = 36
Subtracting 36 from both sides:
x^2 - 9x - 36 = 0
Factoring the quadratic equation:
(x - 12)(x + 3) = 0
Setting each factor to zero:
x - 12 = 0 or x + 3 = 0
x = 12 or x = -3