(2x+9)(3x-4)=0

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Solution for (2x+9)(3x-4)=0 equation: 


Simplifying
(2x + 9)(3x + -4) = 0

Reorder the terms:
(9 + 2x)(3x + -4) = 0

Reorder the terms:
(9 + 2x)(-4 + 3x) = 0

Multiply (9 + 2x) * (-4 + 3x)
(9(-4 + 3x) + 2x * (-4 + 3x)) = 0
((-4 * 9 + 3x * 9) + 2x * (-4 + 3x)) = 0
((-36 + 27x) + 2x * (-4 + 3x)) = 0
(-36 + 27x + (-4 * 2x + 3x * 2x)) = 0
(-36 + 27x + (-8x + 6x2)) = 0

Combine like terms: 27x + -8x = 19x
(-36 + 19x + 6x2) = 0

Solving
-36 + 19x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-9 + -2x)(4 + -3x) = 0


Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5

Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-4.5, 1.333333333}

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