(3x-5)(x-4)=12x-20

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Solution for (3x-5)(x-4)=12x-20 equation: 


Simplifying
(3x + -5)(x + -4) = 12x + -20

Reorder the terms:
(-5 + 3x)(x + -4) = 12x + -20

Reorder the terms:
(-5 + 3x)(-4 + x) = 12x + -20

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

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

Reorder the terms:
20 + -17x + 3x2 = -20 + 12x

Solving
20 + -17x + 3x2 = -20 + 12x

Solving for variable 'x'.

Reorder the terms:
20 + 20 + -17x + -12x + 3x2 = -20 + 12x + 20 + -12x

Combine like terms: 20 + 20 = 40
40 + -17x + -12x + 3x2 = -20 + 12x + 20 + -12x

Combine like terms: -17x + -12x = -29x
40 + -29x + 3x2 = -20 + 12x + 20 + -12x

Reorder the terms:
40 + -29x + 3x2 = -20 + 20 + 12x + -12x

Combine like terms: -20 + 20 = 0
40 + -29x + 3x2 = 0 + 12x + -12x
40 + -29x + 3x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
40 + -29x + 3x2 = 0

Factor a trinomial.
(5 + -3x)(8 + -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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {1.666666667, 8}

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