(6x-11)(3x+7)=0

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Solution for (6x-11)(3x+7)=0 equation: 


Simplifying
(6x + -11)(3x + 7) = 0

Reorder the terms:
(-11 + 6x)(3x + 7) = 0

Reorder the terms:
(-11 + 6x)(7 + 3x) = 0

Multiply (-11 + 6x) * (7 + 3x)
(-11(7 + 3x) + 6x * (7 + 3x)) = 0
((7 * -11 + 3x * -11) + 6x * (7 + 3x)) = 0
((-77 + -33x) + 6x * (7 + 3x)) = 0
(-77 + -33x + (7 * 6x + 3x * 6x)) = 0
(-77 + -33x + (42x + 18x2)) = 0

Combine like terms: -33x + 42x = 9x
(-77 + 9x + 18x2) = 0

Solving
-77 + 9x + 18x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -3x)(11 + -6x) = 0


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

Simplifying
-7 + -3x = 0

Solving
-7 + -3x = 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 + -3x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3x = 0 + 7
-3x = 0 + 7

Combine like terms: 0 + 7 = 7
-3x = 7

Divide each side by '-3'.
x = -2.333333333

Simplifying
x = -2.333333333

Subproblem 2
Set the factor '(11 + -6x)' equal to zero and attempt to solve:

Simplifying
11 + -6x = 0

Solving
11 + -6x = 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 + -6x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -6x = 0 + -11
-6x = 0 + -11

Combine like terms: 0 + -11 = -11
-6x = -11

Divide each side by '-6'.
x = 1.833333333

Simplifying
x = 1.833333333
Solution
x = {-2.333333333, 1.833333333}

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