(4x-9)(3x+1)=0

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Solution for (4x-9)(3x+1)=0 equation: 


Simplifying
(4x + -9)(3x + 1) = 0

Reorder the terms:
(-9 + 4x)(3x + 1) = 0

Reorder the terms:
(-9 + 4x)(1 + 3x) = 0

Multiply (-9 + 4x) * (1 + 3x)
(-9(1 + 3x) + 4x * (1 + 3x)) = 0
((1 * -9 + 3x * -9) + 4x * (1 + 3x)) = 0
((-9 + -27x) + 4x * (1 + 3x)) = 0
(-9 + -27x + (1 * 4x + 3x * 4x)) = 0
(-9 + -27x + (4x + 12x2)) = 0

Combine like terms: -27x + 4x = -23x
(-9 + -23x + 12x2) = 0

Solving
-9 + -23x + 12x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -3x)(9 + -4x) = 0


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

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 2
Set the factor '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 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 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25
Solution
x = {-0.3333333333, 2.25}

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