(4x-13)(3x-2)=0

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Solution for (4x-13)(3x-2)=0 equation: 


Simplifying
(4x + -13)(3x + -2) = 0

Reorder the terms:
(-13 + 4x)(3x + -2) = 0

Reorder the terms:
(-13 + 4x)(-2 + 3x) = 0

Multiply (-13 + 4x) * (-2 + 3x)
(-13(-2 + 3x) + 4x * (-2 + 3x)) = 0
((-2 * -13 + 3x * -13) + 4x * (-2 + 3x)) = 0
((26 + -39x) + 4x * (-2 + 3x)) = 0
(26 + -39x + (-2 * 4x + 3x * 4x)) = 0
(26 + -39x + (-8x + 12x2)) = 0

Combine like terms: -39x + -8x = -47x
(26 + -47x + 12x2) = 0

Solving
26 + -47x + 12x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -3x)(13 + -4x) = 0


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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

Subproblem 2
Set the factor '(13 + -4x)' equal to zero and attempt to solve:

Simplifying
13 + -4x = 0

Solving
13 + -4x = 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 + -4x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -4x = 0 + -13
-4x = 0 + -13

Combine like terms: 0 + -13 = -13
-4x = -13

Divide each side by '-4'.
x = 3.25

Simplifying
x = 3.25
Solution
x = {0.6666666667, 3.25}

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