(3x-5)(x-4)=0

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Solution for (3x-5)(x-4)=0 equation: 


Simplifying
(3x + -5)(x + -4) = 0

Reorder the terms:
(-5 + 3x)(x + -4) = 0

Reorder the terms:
(-5 + 3x)(-4 + x) = 0

Multiply (-5 + 3x) * (-4 + x)
(-5(-4 + x) + 3x * (-4 + x)) = 0
((-4 * -5 + x * -5) + 3x * (-4 + x)) = 0
((20 + -5x) + 3x * (-4 + x)) = 0
(20 + -5x + (-4 * 3x + x * 3x)) = 0
(20 + -5x + (-12x + 3x2)) = 0

Combine like terms: -5x + -12x = -17x
(20 + -17x + 3x2) = 0

Solving
20 + -17x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -3x)(4 + -1x) = 0


Subproblem 1
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {1.666666667, 4}

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