(x-2)(3x)+(2x-1)(x+4)=(5x-1)(x+1)

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Solution for (x-2)(3x)+(2x-1)(x+4)=(5x-1)(x+1) equation:


Simplifying
(x + -2)(3x) + (2x + -1)(x + 4) = (5x + -1)(x + 1)

Reorder the terms:
(-2 + x)(3x) + (2x + -1)(x + 4) = (5x + -1)(x + 1)

Remove parenthesis around (3x)
(-2 + x) * 3x + (2x + -1)(x + 4) = (5x + -1)(x + 1)

Reorder the terms for easier multiplication:
3x(-2 + x) + (2x + -1)(x + 4) = (5x + -1)(x + 1)
(-2 * 3x + x * 3x) + (2x + -1)(x + 4) = (5x + -1)(x + 1)
(-6x + 3x2) + (2x + -1)(x + 4) = (5x + -1)(x + 1)

Reorder the terms:
-6x + 3x2 + (-1 + 2x)(x + 4) = (5x + -1)(x + 1)

Reorder the terms:
-6x + 3x2 + (-1 + 2x)(4 + x) = (5x + -1)(x + 1)

Multiply (-1 + 2x) * (4 + x)
-6x + 3x2 + (-1(4 + x) + 2x * (4 + x)) = (5x + -1)(x + 1)
-6x + 3x2 + ((4 * -1 + x * -1) + 2x * (4 + x)) = (5x + -1)(x + 1)
-6x + 3x2 + ((-4 + -1x) + 2x * (4 + x)) = (5x + -1)(x + 1)
-6x + 3x2 + (-4 + -1x + (4 * 2x + x * 2x)) = (5x + -1)(x + 1)
-6x + 3x2 + (-4 + -1x + (8x + 2x2)) = (5x + -1)(x + 1)

Combine like terms: -1x + 8x = 7x
-6x + 3x2 + (-4 + 7x + 2x2) = (5x + -1)(x + 1)

Reorder the terms:
-4 + -6x + 7x + 3x2 + 2x2 = (5x + -1)(x + 1)

Combine like terms: -6x + 7x = 1x
-4 + 1x + 3x2 + 2x2 = (5x + -1)(x + 1)

Combine like terms: 3x2 + 2x2 = 5x2
-4 + 1x + 5x2 = (5x + -1)(x + 1)

Reorder the terms:
-4 + 1x + 5x2 = (-1 + 5x)(x + 1)

Reorder the terms:
-4 + 1x + 5x2 = (-1 + 5x)(1 + x)

Multiply (-1 + 5x) * (1 + x)
-4 + 1x + 5x2 = (-1(1 + x) + 5x * (1 + x))
-4 + 1x + 5x2 = ((1 * -1 + x * -1) + 5x * (1 + x))
-4 + 1x + 5x2 = ((-1 + -1x) + 5x * (1 + x))
-4 + 1x + 5x2 = (-1 + -1x + (1 * 5x + x * 5x))
-4 + 1x + 5x2 = (-1 + -1x + (5x + 5x2))

Combine like terms: -1x + 5x = 4x
-4 + 1x + 5x2 = (-1 + 4x + 5x2)

Add '-5x2' to each side of the equation.
-4 + 1x + 5x2 + -5x2 = -1 + 4x + 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-4 + 1x + 0 = -1 + 4x + 5x2 + -5x2
-4 + 1x = -1 + 4x + 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-4 + 1x = -1 + 4x + 0
-4 + 1x = -1 + 4x

Solving
-4 + 1x = -1 + 4x

Solving for variable 'x'.

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

Add '-4x' to each side of the equation.
-4 + 1x + -4x = -1 + 4x + -4x

Combine like terms: 1x + -4x = -3x
-4 + -3x = -1 + 4x + -4x

Combine like terms: 4x + -4x = 0
-4 + -3x = -1 + 0
-4 + -3x = -1

Add '4' to each side of the equation.
-4 + 4 + -3x = -1 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = -1 + 4
-3x = -1 + 4

Combine like terms: -1 + 4 = 3
-3x = 3

Divide each side by '-3'.
x = -1

Simplifying
x = -1

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