3x-[(2x+5)-2(x+3)]+4+x^2=(x+3)(x-5)

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Solution for 3x-[(2x+5)-2(x+3)]+4+x^2=(x+3)(x-5) equation: 


Simplifying
3x + -1[(2x + 5) + -2(x + 3)] + 4 + x2 = (x + 3)(x + -5)

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

Remove parenthesis around (5 + 2x)
3x + -1[5 + 2x + -2(x + 3)] + 4 + x2 = (x + 3)(x + -5)

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

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

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

Combine like terms: 2x + -2x = 0
3x + -1[-1 + 0] + 4 + x2 = (x + 3)(x + -5)
3x + -1[-1] + 4 + x2 = (x + 3)(x + -5)

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

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

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

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

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

Multiply (3 + x) * (-5 + x)
5 + 3x + x2 = (3(-5 + x) + x(-5 + x))
5 + 3x + x2 = ((-5 * 3 + x * 3) + x(-5 + x))
5 + 3x + x2 = ((-15 + 3x) + x(-5 + x))
5 + 3x + x2 = (-15 + 3x + (-5 * x + x * x))
5 + 3x + x2 = (-15 + 3x + (-5x + x2))

Combine like terms: 3x + -5x = -2x
5 + 3x + x2 = (-15 + -2x + x2)

Add '-1x2' to each side of the equation.
5 + 3x + x2 + -1x2 = -15 + -2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
5 + 3x + 0 = -15 + -2x + x2 + -1x2
5 + 3x = -15 + -2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
5 + 3x = -15 + -2x + 0
5 + 3x = -15 + -2x

Solving
5 + 3x = -15 + -2x

Solving for variable 'x'.

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

Add '2x' to each side of the equation.
5 + 3x + 2x = -15 + -2x + 2x

Combine like terms: 3x + 2x = 5x
5 + 5x = -15 + -2x + 2x

Combine like terms: -2x + 2x = 0
5 + 5x = -15 + 0
5 + 5x = -15

Add '-5' to each side of the equation.
5 + -5 + 5x = -15 + -5

Combine like terms: 5 + -5 = 0
0 + 5x = -15 + -5
5x = -15 + -5

Combine like terms: -15 + -5 = -20
5x = -20

Divide each side by '5'.
x = -4

Simplifying
x = -4

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