-3x(x+9)=42

Solution for -3x(x+9)=42 equation:

Simplifying
-3x(x + 9) = 42

Reorder the terms:
-3x(9 + x) = 42
(9 * -3x + x * -3x) = 42
(-27x + -3x2) = 42

Solving
-27x + -3x2 = 42

Solving for variable 'x'.

Reorder the terms:
-42 + -27x + -3x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + -27x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(14 + 9x + x2) = 0

Factor a trinomial.
-3((7 + x)(2 + x)) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-7, -2}