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

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


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

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

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

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

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

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

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

Add '-2x2' to each side of the equation.
3 + 2x + 2x2 + -2x2 = -6 + -4x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
3 + 2x + 0 = -6 + -4x + 2x2 + -2x2
3 + 2x = -6 + -4x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
3 + 2x = -6 + -4x + 0
3 + 2x = -6 + -4x

Solving
3 + 2x = -6 + -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.
3 + 2x + 4x = -6 + -4x + 4x

Combine like terms: 2x + 4x = 6x
3 + 6x = -6 + -4x + 4x

Combine like terms: -4x + 4x = 0
3 + 6x = -6 + 0
3 + 6x = -6

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

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

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

Divide each side by '6'.
x = -1.5

Simplifying
x = -1.5

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