[x-4][4x-3]+3=0

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Solution for [x-4][4x-3]+3=0 equation: 


Simplifying
[x + -4][4x + -3] + 3 = 0

Reorder the terms:
[-4 + x][4x + -3] + 3 = 0

Reorder the terms:
[-4 + x][-3 + 4x] + 3 = 0

Multiply [-4 + x] * [-3 + 4x]
[-4[-3 + 4x] + x[-3 + 4x]] + 3 = 0
[[-3 * -4 + 4x * -4] + x[-3 + 4x]] + 3 = 0
[[12 + -16x] + x[-3 + 4x]] + 3 = 0
[12 + -16x + [-3 * x + 4x * x]] + 3 = 0
[12 + -16x + [-3x + 4x2]] + 3 = 0

Combine like terms: -16x + -3x = -19x
[12 + -19x + 4x2] + 3 = 0

Reorder the terms:
12 + 3 + -19x + 4x2 = 0

Combine like terms: 12 + 3 = 15
15 + -19x + 4x2 = 0

Solving
15 + -19x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(15 + -4x) = 0


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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(15 + -4x)' equal to zero and attempt to solve:

Simplifying
15 + -4x = 0

Solving
15 + -4x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -4x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -4x = 0 + -15
-4x = 0 + -15

Combine like terms: 0 + -15 = -15
-4x = -15

Divide each side by '-4'.
x = 3.75

Simplifying
x = 3.75
Solution
x = {1, 3.75}

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