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

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


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

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

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

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

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

Solving
0 = 20 + -17x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -20 = -20
-20 + 17x + -3x2 = 20 + -17x + 3x2 + -20 + 17x + -3x2

Reorder the terms:
-20 + 17x + -3x2 = 20 + -20 + -17x + 17x + 3x2 + -3x2

Combine like terms: 20 + -20 = 0
-20 + 17x + -3x2 = 0 + -17x + 17x + 3x2 + -3x2
-20 + 17x + -3x2 = -17x + 17x + 3x2 + -3x2

Combine like terms: -17x + 17x = 0
-20 + 17x + -3x2 = 0 + 3x2 + -3x2
-20 + 17x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-20 + 17x + -3x2 = 0

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


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

Simplifying
-4 + x = 0

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

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

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

Simplifying
x = 4

Subproblem 2
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
Solution
x = {4, 1.666666667}

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