(3x+1)(x-4)-5(x-4)=0

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Solution for (3x+1)(x-4)-5(x-4)=0 equation: 


Simplifying
(3x + 1)(x + -4) + -5(x + -4) = 0

Reorder the terms:
(1 + 3x)(x + -4) + -5(x + -4) = 0

Reorder the terms:
(1 + 3x)(-4 + x) + -5(x + -4) = 0

Multiply (1 + 3x) * (-4 + x)
(1(-4 + x) + 3x * (-4 + x)) + -5(x + -4) = 0
((-4 * 1 + x * 1) + 3x * (-4 + x)) + -5(x + -4) = 0
((-4 + 1x) + 3x * (-4 + x)) + -5(x + -4) = 0
(-4 + 1x + (-4 * 3x + x * 3x)) + -5(x + -4) = 0
(-4 + 1x + (-12x + 3x2)) + -5(x + -4) = 0

Combine like terms: 1x + -12x = -11x
(-4 + -11x + 3x2) + -5(x + -4) = 0

Reorder the terms:
-4 + -11x + 3x2 + -5(-4 + x) = 0
-4 + -11x + 3x2 + (-4 * -5 + x * -5) = 0
-4 + -11x + 3x2 + (20 + -5x) = 0

Reorder the terms:
-4 + 20 + -11x + -5x + 3x2 = 0

Combine like terms: -4 + 20 = 16
16 + -11x + -5x + 3x2 = 0

Combine like terms: -11x + -5x = -16x
16 + -16x + 3x2 = 0

Solving
16 + -16x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -3x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {1.333333333, 4}

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