(x-4)(3x-5)=48

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Solution for (x-4)(3x-5)=48 equation: 


Simplifying
(x + -4)(3x + -5) = 48

Reorder the terms:
(-4 + x)(3x + -5) = 48

Reorder the terms:
(-4 + x)(-5 + 3x) = 48

Multiply (-4 + x) * (-5 + 3x)
(-4(-5 + 3x) + x(-5 + 3x)) = 48
((-5 * -4 + 3x * -4) + x(-5 + 3x)) = 48
((20 + -12x) + x(-5 + 3x)) = 48
(20 + -12x + (-5 * x + 3x * x)) = 48
(20 + -12x + (-5x + 3x2)) = 48

Combine like terms: -12x + -5x = -17x
(20 + -17x + 3x2) = 48

Solving
20 + -17x + 3x2 = 48

Solving for variable 'x'.

Reorder the terms:
20 + -48 + -17x + 3x2 = 48 + -48

Combine like terms: 20 + -48 = -28
-28 + -17x + 3x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-28 + -17x + 3x2 = 0

Factor a trinomial.
(-4 + -3x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 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 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-1.333333333, 7}

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