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

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

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

Reorder the terms:
3x(-3 + x) + -1(x + -4) = 1
(-3 * 3x + x * 3x) + -1(x + -4) = 1
(-9x + 3x2) + -1(x + -4) = 1

Reorder the terms:
-9x + 3x2 + -1(-4 + x) = 1
-9x + 3x2 + (-4 * -1 + x * -1) = 1
-9x + 3x2 + (4 + -1x) = 1

Reorder the terms:
4 + -9x + -1x + 3x2 = 1

Combine like terms: -9x + -1x = -10x
4 + -10x + 3x2 = 1

Solving
4 + -10x + 3x2 = 1

Solving for variable 'x'.

Reorder the terms:
4 + -1 + -10x + 3x2 = 1 + -1

Combine like terms: 4 + -1 = 3
3 + -10x + 3x2 = 1 + -1

Combine like terms: 1 + -1 = 0
3 + -10x + 3x2 = 0

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

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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
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 = {0.3333333333, 3}