(2x-1)(x+3)=6x-x(x+1)

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Solution for (2x-1)(x+3)=6x-x(x+1) equation: 


Simplifying
(2x + -1)(x + 3) = 6x + -1x(x + 1)

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

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

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

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

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

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

Add '-5x' to each side of the equation.
-3 + 5x + -5x + 2x2 = 5x + -5x + -1x2

Combine like terms: 5x + -5x = 0
-3 + 0 + 2x2 = 5x + -5x + -1x2
-3 + 2x2 = 5x + -5x + -1x2

Combine like terms: 5x + -5x = 0
-3 + 2x2 = 0 + -1x2
-3 + 2x2 = -1x2

Solving
-3 + 2x2 = -1x2

Solving for variable 'x'.

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

Add 'x2' to each side of the equation.
-3 + 2x2 + x2 = -1x2 + x2

Combine like terms: 2x2 + x2 = 3x2
-3 + 3x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-3 + 3x2 = 0

Add '3' to each side of the equation.
-3 + 3 + 3x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 3x2 = 0 + 3
3x2 = 0 + 3

Combine like terms: 0 + 3 = 3
3x2 = 3

Divide each side by '3'.
x2 = 1

Simplifying
x2 = 1

Take the square root of each side:
x = {-1, 1}

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