9(x+7)(3x-1)=0

Solution for 9(x+7)(3x-1)=0 equation:

Simplifying
9(x + 7)(3x + -1) = 0

Reorder the terms:
9(7 + x)(3x + -1) = 0

Reorder the terms:
9(7 + x)(-1 + 3x) = 0

Multiply (7 + x) * (-1 + 3x)
9(7(-1 + 3x) + x(-1 + 3x)) = 0
9((-1 * 7 + 3x * 7) + x(-1 + 3x)) = 0
9((-7 + 21x) + x(-1 + 3x)) = 0
9(-7 + 21x + (-1 * x + 3x * x)) = 0
9(-7 + 21x + (-1x + 3x2)) = 0

Combine like terms: 21x + -1x = 20x
9(-7 + 20x + 3x2) = 0
(-7 * 9 + 20x * 9 + 3x2 * 9) = 0
(-63 + 180x + 27x2) = 0

Solving
-63 + 180x + 27x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-7 + 20x + 3x2) = 0

Factor a trinomial.
9((-7 + -1x)(1 + -3x)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 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 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-7, 0.3333333333}