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

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


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

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

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

Multiply (3 + 4x) * (-4 + x)
(3(-4 + x) + 4x * (-4 + x)) + -1(x + -1)(x + -3) = 3x(x + -2)
((-4 * 3 + x * 3) + 4x * (-4 + x)) + -1(x + -1)(x + -3) = 3x(x + -2)
((-12 + 3x) + 4x * (-4 + x)) + -1(x + -1)(x + -3) = 3x(x + -2)
(-12 + 3x + (-4 * 4x + x * 4x)) + -1(x + -1)(x + -3) = 3x(x + -2)
(-12 + 3x + (-16x + 4x2)) + -1(x + -1)(x + -3) = 3x(x + -2)

Combine like terms: 3x + -16x = -13x
(-12 + -13x + 4x2) + -1(x + -1)(x + -3) = 3x(x + -2)

Reorder the terms:
-12 + -13x + 4x2 + -1(-1 + x)(x + -3) = 3x(x + -2)

Reorder the terms:
-12 + -13x + 4x2 + -1(-1 + x)(-3 + x) = 3x(x + -2)

Multiply (-1 + x) * (-3 + x)
-12 + -13x + 4x2 + -1(-1(-3 + x) + x(-3 + x)) = 3x(x + -2)
-12 + -13x + 4x2 + -1((-3 * -1 + x * -1) + x(-3 + x)) = 3x(x + -2)
-12 + -13x + 4x2 + -1((3 + -1x) + x(-3 + x)) = 3x(x + -2)
-12 + -13x + 4x2 + -1(3 + -1x + (-3 * x + x * x)) = 3x(x + -2)
-12 + -13x + 4x2 + -1(3 + -1x + (-3x + x2)) = 3x(x + -2)

Combine like terms: -1x + -3x = -4x
-12 + -13x + 4x2 + -1(3 + -4x + x2) = 3x(x + -2)
-12 + -13x + 4x2 + (3 * -1 + -4x * -1 + x2 * -1) = 3x(x + -2)
-12 + -13x + 4x2 + (-3 + 4x + -1x2) = 3x(x + -2)

Reorder the terms:
-12 + -3 + -13x + 4x + 4x2 + -1x2 = 3x(x + -2)

Combine like terms: -12 + -3 = -15
-15 + -13x + 4x + 4x2 + -1x2 = 3x(x + -2)

Combine like terms: -13x + 4x = -9x
-15 + -9x + 4x2 + -1x2 = 3x(x + -2)

Combine like terms: 4x2 + -1x2 = 3x2
-15 + -9x + 3x2 = 3x(x + -2)

Reorder the terms:
-15 + -9x + 3x2 = 3x(-2 + x)
-15 + -9x + 3x2 = (-2 * 3x + x * 3x)
-15 + -9x + 3x2 = (-6x + 3x2)

Add '-3x2' to each side of the equation.
-15 + -9x + 3x2 + -3x2 = -6x + 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-15 + -9x + 0 = -6x + 3x2 + -3x2
-15 + -9x = -6x + 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-15 + -9x = -6x + 0
-15 + -9x = -6x

Solving
-15 + -9x = -6x

Solving for variable 'x'.

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

Add '6x' to each side of the equation.
-15 + -9x + 6x = -6x + 6x

Combine like terms: -9x + 6x = -3x
-15 + -3x = -6x + 6x

Combine like terms: -6x + 6x = 0
-15 + -3x = 0

Add '15' to each side of the equation.
-15 + 15 + -3x = 0 + 15

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

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

Divide each side by '-3'.
x = -5

Simplifying
x = -5

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