(2x+9)(3x-11)=-8

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Solution for (2x+9)(3x-11)=-8 equation: 


Simplifying
(2x + 9)(3x + -11) = -8

Reorder the terms:
(9 + 2x)(3x + -11) = -8

Reorder the terms:
(9 + 2x)(-11 + 3x) = -8

Multiply (9 + 2x) * (-11 + 3x)
(9(-11 + 3x) + 2x * (-11 + 3x)) = -8
((-11 * 9 + 3x * 9) + 2x * (-11 + 3x)) = -8
((-99 + 27x) + 2x * (-11 + 3x)) = -8
(-99 + 27x + (-11 * 2x + 3x * 2x)) = -8
(-99 + 27x + (-22x + 6x2)) = -8

Combine like terms: 27x + -22x = 5x
(-99 + 5x + 6x2) = -8

Solving
-99 + 5x + 6x2 = -8

Solving for variable 'x'.

Reorder the terms:
-99 + 8 + 5x + 6x2 = -8 + 8

Combine like terms: -99 + 8 = -91
-91 + 5x + 6x2 = -8 + 8

Combine like terms: -8 + 8 = 0
-91 + 5x + 6x2 = 0

Factor a trinomial.
(-13 + -3x)(7 + -2x) = 0


Subproblem 1
Set the factor '(-13 + -3x)' equal to zero and attempt to solve:

Simplifying
-13 + -3x = 0

Solving
-13 + -3x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -3x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -3x = 0 + 13
-3x = 0 + 13

Combine like terms: 0 + 13 = 13
-3x = 13

Divide each side by '-3'.
x = -4.333333333

Simplifying
x = -4.333333333

Subproblem 2
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
Solution
x = {-4.333333333, 3.5}

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