(3x+9)(7x-2)=0

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Solution for (3x+9)(7x-2)=0 equation: 


Simplifying
(3x + 9)(7x + -2) = 0

Reorder the terms:
(9 + 3x)(7x + -2) = 0

Reorder the terms:
(9 + 3x)(-2 + 7x) = 0

Multiply (9 + 3x) * (-2 + 7x)
(9(-2 + 7x) + 3x * (-2 + 7x)) = 0
((-2 * 9 + 7x * 9) + 3x * (-2 + 7x)) = 0
((-18 + 63x) + 3x * (-2 + 7x)) = 0
(-18 + 63x + (-2 * 3x + 7x * 3x)) = 0
(-18 + 63x + (-6x + 21x2)) = 0

Combine like terms: 63x + -6x = 57x
(-18 + 57x + 21x2) = 0

Solving
-18 + 57x + 21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + 19x + 7x2) = 0

Factor a trinomial.
3((-3 + -1x)(2 + -7x)) = 0

Ignore the factor 3.

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = -3

Simplifying
x = -3

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

Simplifying
2 + -7x = 0

Solving
2 + -7x = 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 + -7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7x = 0 + -2
-7x = 0 + -2

Combine like terms: 0 + -2 = -2
-7x = -2

Divide each side by '-7'.
x = 0.2857142857

Simplifying
x = 0.2857142857
Solution
x = {-3, 0.2857142857}

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