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

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


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

Reorder the terms:
3(-1 + x) + -2x(4 + -1x) = (2x + 1)(x + -3)
(-1 * 3 + x * 3) + -2x(4 + -1x) = (2x + 1)(x + -3)
(-3 + 3x) + -2x(4 + -1x) = (2x + 1)(x + -3)
-3 + 3x + (4 * -2x + -1x * -2x) = (2x + 1)(x + -3)
-3 + 3x + (-8x + 2x2) = (2x + 1)(x + -3)

Combine like terms: 3x + -8x = -5x
-3 + -5x + 2x2 = (2x + 1)(x + -3)

Reorder the terms:
-3 + -5x + 2x2 = (1 + 2x)(x + -3)

Reorder the terms:
-3 + -5x + 2x2 = (1 + 2x)(-3 + x)

Multiply (1 + 2x) * (-3 + x)
-3 + -5x + 2x2 = (1(-3 + x) + 2x * (-3 + x))
-3 + -5x + 2x2 = ((-3 * 1 + x * 1) + 2x * (-3 + x))
-3 + -5x + 2x2 = ((-3 + 1x) + 2x * (-3 + x))
-3 + -5x + 2x2 = (-3 + 1x + (-3 * 2x + x * 2x))
-3 + -5x + 2x2 = (-3 + 1x + (-6x + 2x2))

Combine like terms: 1x + -6x = -5x
-3 + -5x + 2x2 = (-3 + -5x + 2x2)

Add '3' to each side of the equation.
-3 + -5x + 3 + 2x2 = -3 + -5x + 3 + 2x2

Reorder the terms:
-3 + 3 + -5x + 2x2 = -3 + -5x + 3 + 2x2

Combine like terms: -3 + 3 = 0
0 + -5x + 2x2 = -3 + -5x + 3 + 2x2
-5x + 2x2 = -3 + -5x + 3 + 2x2

Reorder the terms:
-5x + 2x2 = -3 + 3 + -5x + 2x2

Combine like terms: -3 + 3 = 0
-5x + 2x2 = 0 + -5x + 2x2
-5x + 2x2 = -5x + 2x2

Add '5x' to each side of the equation.
-5x + 5x + 2x2 = -5x + 5x + 2x2

Combine like terms: -5x + 5x = 0
0 + 2x2 = -5x + 5x + 2x2
2x2 = -5x + 5x + 2x2

Combine like terms: -5x + 5x = 0
2x2 = 0 + 2x2
2x2 = 2x2

Add '-2x2' to each side of the equation.
2x2 + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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