4(x-2)(x-1)-3(x-2)=3

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Solution for 4(x-2)(x-1)-3(x-2)=3 equation: 


Simplifying
4(x + -2)(x + -1) + -3(x + -2) = 3

Reorder the terms:
4(-2 + x)(x + -1) + -3(x + -2) = 3

Reorder the terms:
4(-2 + x)(-1 + x) + -3(x + -2) = 3

Multiply (-2 + x) * (-1 + x)
4(-2(-1 + x) + x(-1 + x)) + -3(x + -2) = 3
4((-1 * -2 + x * -2) + x(-1 + x)) + -3(x + -2) = 3
4((2 + -2x) + x(-1 + x)) + -3(x + -2) = 3
4(2 + -2x + (-1 * x + x * x)) + -3(x + -2) = 3
4(2 + -2x + (-1x + x2)) + -3(x + -2) = 3

Combine like terms: -2x + -1x = -3x
4(2 + -3x + x2) + -3(x + -2) = 3
(2 * 4 + -3x * 4 + x2 * 4) + -3(x + -2) = 3
(8 + -12x + 4x2) + -3(x + -2) = 3

Reorder the terms:
8 + -12x + 4x2 + -3(-2 + x) = 3
8 + -12x + 4x2 + (-2 * -3 + x * -3) = 3
8 + -12x + 4x2 + (6 + -3x) = 3

Reorder the terms:
8 + 6 + -12x + -3x + 4x2 = 3

Combine like terms: 8 + 6 = 14
14 + -12x + -3x + 4x2 = 3

Combine like terms: -12x + -3x = -15x
14 + -15x + 4x2 = 3

Solving
14 + -15x + 4x2 = 3

Solving for variable 'x'.

Reorder the terms:
14 + -3 + -15x + 4x2 = 3 + -3

Combine like terms: 14 + -3 = 11
11 + -15x + 4x2 = 3 + -3

Combine like terms: 3 + -3 = 0
11 + -15x + 4x2 = 0

Factor a trinomial.
(1 + -1x)(11 + -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 '(11 + -4x)' equal to zero and attempt to solve:

Simplifying
11 + -4x = 0

Solving
11 + -4x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -4x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -4x = 0 + -11
-4x = 0 + -11

Combine like terms: 0 + -11 = -11
-4x = -11

Divide each side by '-4'.
x = 2.75

Simplifying
x = 2.75
Solution
x = {1, 2.75}

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