(3x+9)(7x-11)=0

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Solution for (3x+9)(7x-11)=0 equation: 


Simplifying
(3x + 9)(7x + -11) = 0

Reorder the terms:
(9 + 3x)(7x + -11) = 0

Reorder the terms:
(9 + 3x)(-11 + 7x) = 0

Multiply (9 + 3x) * (-11 + 7x)
(9(-11 + 7x) + 3x * (-11 + 7x)) = 0
((-11 * 9 + 7x * 9) + 3x * (-11 + 7x)) = 0
((-99 + 63x) + 3x * (-11 + 7x)) = 0
(-99 + 63x + (-11 * 3x + 7x * 3x)) = 0
(-99 + 63x + (-33x + 21x2)) = 0

Combine like terms: 63x + -33x = 30x
(-99 + 30x + 21x2) = 0

Solving
-99 + 30x + 21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-33 + 10x + 7x2) = 0

Factor a trinomial.
3((-3 + -1x)(11 + -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 '(11 + -7x)' equal to zero and attempt to solve:

Simplifying
11 + -7x = 0

Solving
11 + -7x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -7x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -7x = 0 + -11
-7x = 0 + -11

Combine like terms: 0 + -11 = -11
-7x = -11

Divide each side by '-7'.
x = 1.571428571

Simplifying
x = 1.571428571
Solution
x = {-3, 1.571428571}

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