(6x+9)(4x-11)=0

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Solution for (6x+9)(4x-11)=0 equation: 


Simplifying
(6x + 9)(4x + -11) = 0

Reorder the terms:
(9 + 6x)(4x + -11) = 0

Reorder the terms:
(9 + 6x)(-11 + 4x) = 0

Multiply (9 + 6x) * (-11 + 4x)
(9(-11 + 4x) + 6x * (-11 + 4x)) = 0
((-11 * 9 + 4x * 9) + 6x * (-11 + 4x)) = 0
((-99 + 36x) + 6x * (-11 + 4x)) = 0
(-99 + 36x + (-11 * 6x + 4x * 6x)) = 0
(-99 + 36x + (-66x + 24x2)) = 0

Combine like terms: 36x + -66x = -30x
(-99 + -30x + 24x2) = 0

Solving
-99 + -30x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-33 + -10x + 8x2) = 0

Factor a trinomial.
3((-3 + -2x)(11 + -4x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
Set the factor '(11 + -4x)' equal to zero and attempt to solve:

Simplifying
11 + -4x = 0

Solving
11 + -4x = 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 + -4x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -4x = 0 + -11
-4x = 0 + -11

Combine like terms: 0 + -11 = -11
-4x = -11

Divide each side by '-4'.
x = 2.75

Simplifying
x = 2.75
Solution
x = {-1.5, 2.75}

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