(2x-6)(x-4)=84

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Solution for (2x-6)(x-4)=84 equation: 


Simplifying
(2x + -6)(x + -4) = 84

Reorder the terms:
(-6 + 2x)(x + -4) = 84

Reorder the terms:
(-6 + 2x)(-4 + x) = 84

Multiply (-6 + 2x) * (-4 + x)
(-6(-4 + x) + 2x * (-4 + x)) = 84
((-4 * -6 + x * -6) + 2x * (-4 + x)) = 84
((24 + -6x) + 2x * (-4 + x)) = 84
(24 + -6x + (-4 * 2x + x * 2x)) = 84
(24 + -6x + (-8x + 2x2)) = 84

Combine like terms: -6x + -8x = -14x
(24 + -14x + 2x2) = 84

Solving
24 + -14x + 2x2 = 84

Solving for variable 'x'.

Reorder the terms:
24 + -84 + -14x + 2x2 = 84 + -84

Combine like terms: 24 + -84 = -60
-60 + -14x + 2x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-60 + -14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + -7x + x2) = 0

Factor a trinomial.
2((-3 + -1x)(10 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-3, 10}

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