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

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


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

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

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

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

Combine like terms: -2x + 1x = -1x
3(-2 + -1x + x2) + -4 = 2(x + -1)(x + -1)
(-2 * 3 + -1x * 3 + x2 * 3) + -4 = 2(x + -1)(x + -1)
(-6 + -3x + 3x2) + -4 = 2(x + -1)(x + -1)

Reorder the terms:
-6 + -4 + -3x + 3x2 = 2(x + -1)(x + -1)

Combine like terms: -6 + -4 = -10
-10 + -3x + 3x2 = 2(x + -1)(x + -1)

Reorder the terms:
-10 + -3x + 3x2 = 2(-1 + x)(x + -1)

Reorder the terms:
-10 + -3x + 3x2 = 2(-1 + x)(-1 + x)

Multiply (-1 + x) * (-1 + x)
-10 + -3x + 3x2 = 2(-1(-1 + x) + x(-1 + x))
-10 + -3x + 3x2 = 2((-1 * -1 + x * -1) + x(-1 + x))
-10 + -3x + 3x2 = 2((1 + -1x) + x(-1 + x))
-10 + -3x + 3x2 = 2(1 + -1x + (-1 * x + x * x))
-10 + -3x + 3x2 = 2(1 + -1x + (-1x + x2))

Combine like terms: -1x + -1x = -2x
-10 + -3x + 3x2 = 2(1 + -2x + x2)
-10 + -3x + 3x2 = (1 * 2 + -2x * 2 + x2 * 2)
-10 + -3x + 3x2 = (2 + -4x + 2x2)

Solving
-10 + -3x + 3x2 = 2 + -4x + 2x2

Solving for variable 'x'.

Reorder the terms:
-10 + -2 + -3x + 4x + 3x2 + -2x2 = 2 + -4x + 2x2 + -2 + 4x + -2x2

Combine like terms: -10 + -2 = -12
-12 + -3x + 4x + 3x2 + -2x2 = 2 + -4x + 2x2 + -2 + 4x + -2x2

Combine like terms: -3x + 4x = 1x
-12 + 1x + 3x2 + -2x2 = 2 + -4x + 2x2 + -2 + 4x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-12 + 1x + 1x2 = 2 + -4x + 2x2 + -2 + 4x + -2x2

Reorder the terms:
-12 + 1x + 1x2 = 2 + -2 + -4x + 4x + 2x2 + -2x2

Combine like terms: 2 + -2 = 0
-12 + 1x + 1x2 = 0 + -4x + 4x + 2x2 + -2x2
-12 + 1x + 1x2 = -4x + 4x + 2x2 + -2x2

Combine like terms: -4x + 4x = 0
-12 + 1x + 1x2 = 0 + 2x2 + -2x2
-12 + 1x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-12 + 1x + 1x2 = 0

Factor a trinomial.
(-4 + -1x)(3 + -1x) = 0


Subproblem 1
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

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 = {-4, 3}

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