(x-4)(x-1)=3x-11

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Solution for (x-4)(x-1)=3x-11 equation: 


Simplifying
(x + -4)(x + -1) = 3x + -11

Reorder the terms:
(-4 + x)(x + -1) = 3x + -11

Reorder the terms:
(-4 + x)(-1 + x) = 3x + -11

Multiply (-4 + x) * (-1 + x)
(-4(-1 + x) + x(-1 + x)) = 3x + -11
((-1 * -4 + x * -4) + x(-1 + x)) = 3x + -11
((4 + -4x) + x(-1 + x)) = 3x + -11
(4 + -4x + (-1 * x + x * x)) = 3x + -11
(4 + -4x + (-1x + x2)) = 3x + -11

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

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

Solving
4 + -5x + x2 = -11 + 3x

Solving for variable 'x'.

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

Combine like terms: 4 + 11 = 15
15 + -5x + -3x + x2 = -11 + 3x + 11 + -3x

Combine like terms: -5x + -3x = -8x
15 + -8x + x2 = -11 + 3x + 11 + -3x

Reorder the terms:
15 + -8x + x2 = -11 + 11 + 3x + -3x

Combine like terms: -11 + 11 = 0
15 + -8x + x2 = 0 + 3x + -3x
15 + -8x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
15 + -8x + x2 = 0

Factor a trinomial.
(3 + -1x)(5 + -1x) = 0


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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {3, 5}

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