(3x-4)(x-2)-5=0

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Solution for (3x-4)(x-2)-5=0 equation: 


Simplifying
(3x + -4)(x + -2) + -5 = 0

Reorder the terms:
(-4 + 3x)(x + -2) + -5 = 0

Reorder the terms:
(-4 + 3x)(-2 + x) + -5 = 0

Multiply (-4 + 3x) * (-2 + x)
(-4(-2 + x) + 3x * (-2 + x)) + -5 = 0
((-2 * -4 + x * -4) + 3x * (-2 + x)) + -5 = 0
((8 + -4x) + 3x * (-2 + x)) + -5 = 0
(8 + -4x + (-2 * 3x + x * 3x)) + -5 = 0
(8 + -4x + (-6x + 3x2)) + -5 = 0

Combine like terms: -4x + -6x = -10x
(8 + -10x + 3x2) + -5 = 0

Reorder the terms:
8 + -5 + -10x + 3x2 = 0

Combine like terms: 8 + -5 = 3
3 + -10x + 3x2 = 0

Solving
3 + -10x + 3x2 = 0

Solving for variable 'x'.

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.3333333333, 3}

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