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

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


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

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

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

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

Combine like terms: 9 + 3 = 12
12 + -3x + -3x = -4(x + -1)(x + -3)

Combine like terms: -3x + -3x = -6x
12 + -6x = -4(x + -1)(x + -3)

Reorder the terms:
12 + -6x = -4(-1 + x)(x + -3)

Reorder the terms:
12 + -6x = -4(-1 + x)(-3 + x)

Multiply (-1 + x) * (-3 + x)
12 + -6x = -4(-1(-3 + x) + x(-3 + x))
12 + -6x = -4((-3 * -1 + x * -1) + x(-3 + x))
12 + -6x = -4((3 + -1x) + x(-3 + x))
12 + -6x = -4(3 + -1x + (-3 * x + x * x))
12 + -6x = -4(3 + -1x + (-3x + x2))

Combine like terms: -1x + -3x = -4x
12 + -6x = -4(3 + -4x + x2)
12 + -6x = (3 * -4 + -4x * -4 + x2 * -4)
12 + -6x = (-12 + 16x + -4x2)

Solving
12 + -6x = -12 + 16x + -4x2

Solving for variable 'x'.

Reorder the terms:
12 + 12 + -6x + -16x + 4x2 = -12 + 16x + -4x2 + 12 + -16x + 4x2

Combine like terms: 12 + 12 = 24
24 + -6x + -16x + 4x2 = -12 + 16x + -4x2 + 12 + -16x + 4x2

Combine like terms: -6x + -16x = -22x
24 + -22x + 4x2 = -12 + 16x + -4x2 + 12 + -16x + 4x2

Reorder the terms:
24 + -22x + 4x2 = -12 + 12 + 16x + -16x + -4x2 + 4x2

Combine like terms: -12 + 12 = 0
24 + -22x + 4x2 = 0 + 16x + -16x + -4x2 + 4x2
24 + -22x + 4x2 = 16x + -16x + -4x2 + 4x2

Combine like terms: 16x + -16x = 0
24 + -22x + 4x2 = 0 + -4x2 + 4x2
24 + -22x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
24 + -22x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -11x + 2x2) = 0

Factor a trinomial.
2((3 + -2x)(4 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

Subproblem 2
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
Solution
x = {1.5, 4}

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