(3x-1)(4x-2)=80

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Solution for (3x-1)(4x-2)=80 equation: 


Simplifying
(3x + -1)(4x + -2) = 80

Reorder the terms:
(-1 + 3x)(4x + -2) = 80

Reorder the terms:
(-1 + 3x)(-2 + 4x) = 80

Multiply (-1 + 3x) * (-2 + 4x)
(-1(-2 + 4x) + 3x * (-2 + 4x)) = 80
((-2 * -1 + 4x * -1) + 3x * (-2 + 4x)) = 80
((2 + -4x) + 3x * (-2 + 4x)) = 80
(2 + -4x + (-2 * 3x + 4x * 3x)) = 80
(2 + -4x + (-6x + 12x2)) = 80

Combine like terms: -4x + -6x = -10x
(2 + -10x + 12x2) = 80

Solving
2 + -10x + 12x2 = 80

Solving for variable 'x'.

Reorder the terms:
2 + -80 + -10x + 12x2 = 80 + -80

Combine like terms: 2 + -80 = -78
-78 + -10x + 12x2 = 80 + -80

Combine like terms: 80 + -80 = 0
-78 + -10x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-39 + -5x + 6x2) = 0

Factor a trinomial.
2((-13 + -6x)(3 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-13 + -6x)' equal to zero and attempt to solve:

Simplifying
-13 + -6x = 0

Solving
-13 + -6x = 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 + -6x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -6x = 0 + 13
-6x = 0 + 13

Combine like terms: 0 + 13 = 13
-6x = 13

Divide each side by '-6'.
x = -2.166666667

Simplifying
x = -2.166666667

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 = {-2.166666667, 3}

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