(2x+7)(3x-11)=0

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Solution for (2x+7)(3x-11)=0 equation: 


Simplifying
(2x + 7)(3x + -11) = 0

Reorder the terms:
(7 + 2x)(3x + -11) = 0

Reorder the terms:
(7 + 2x)(-11 + 3x) = 0

Multiply (7 + 2x) * (-11 + 3x)
(7(-11 + 3x) + 2x * (-11 + 3x)) = 0
((-11 * 7 + 3x * 7) + 2x * (-11 + 3x)) = 0
((-77 + 21x) + 2x * (-11 + 3x)) = 0
(-77 + 21x + (-11 * 2x + 3x * 2x)) = 0
(-77 + 21x + (-22x + 6x2)) = 0

Combine like terms: 21x + -22x = -1x
(-77 + -1x + 6x2) = 0

Solving
-77 + -1x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -2x)(11 + -3x) = 0


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

Simplifying
-7 + -2x = 0

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

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

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

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

Subproblem 2
Set the factor '(11 + -3x)' equal to zero and attempt to solve:

Simplifying
11 + -3x = 0

Solving
11 + -3x = 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 + -3x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3x = 0 + -11
-3x = 0 + -11

Combine like terms: 0 + -11 = -11
-3x = -11

Divide each side by '-3'.
x = 3.666666667

Simplifying
x = 3.666666667
Solution
x = {-3.5, 3.666666667}

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