(3x-1)-5(x+2)(x-2)+12=6+(2x+3)

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Solution for (3x-1)-5(x+2)(x-2)+12=6+(2x+3) equation: 


Simplifying
(3x + -1) + -5(x + 2)(x + -2) + 12 = 6 + (2x + 3)

Reorder the terms:
(-1 + 3x) + -5(x + 2)(x + -2) + 12 = 6 + (2x + 3)

Remove parenthesis around (-1 + 3x)
-1 + 3x + -5(x + 2)(x + -2) + 12 = 6 + (2x + 3)

Reorder the terms:
-1 + 3x + -5(2 + x)(x + -2) + 12 = 6 + (2x + 3)

Reorder the terms:
-1 + 3x + -5(2 + x)(-2 + x) + 12 = 6 + (2x + 3)

Multiply (2 + x) * (-2 + x)
-1 + 3x + -5(2(-2 + x) + x(-2 + x)) + 12 = 6 + (2x + 3)
-1 + 3x + -5((-2 * 2 + x * 2) + x(-2 + x)) + 12 = 6 + (2x + 3)
-1 + 3x + -5((-4 + 2x) + x(-2 + x)) + 12 = 6 + (2x + 3)
-1 + 3x + -5(-4 + 2x + (-2 * x + x * x)) + 12 = 6 + (2x + 3)
-1 + 3x + -5(-4 + 2x + (-2x + x2)) + 12 = 6 + (2x + 3)

Combine like terms: 2x + -2x = 0
-1 + 3x + -5(-4 + 0 + x2) + 12 = 6 + (2x + 3)
-1 + 3x + -5(-4 + x2) + 12 = 6 + (2x + 3)
-1 + 3x + (-4 * -5 + x2 * -5) + 12 = 6 + (2x + 3)
-1 + 3x + (20 + -5x2) + 12 = 6 + (2x + 3)

Reorder the terms:
-1 + 20 + 12 + 3x + -5x2 = 6 + (2x + 3)

Combine like terms: -1 + 20 = 19
19 + 12 + 3x + -5x2 = 6 + (2x + 3)

Combine like terms: 19 + 12 = 31
31 + 3x + -5x2 = 6 + (2x + 3)

Reorder the terms:
31 + 3x + -5x2 = 6 + (3 + 2x)

Remove parenthesis around (3 + 2x)
31 + 3x + -5x2 = 6 + 3 + 2x

Combine like terms: 6 + 3 = 9
31 + 3x + -5x2 = 9 + 2x

Solving
31 + 3x + -5x2 = 9 + 2x

Solving for variable 'x'.

Reorder the terms:
31 + -9 + 3x + -2x + -5x2 = 9 + 2x + -9 + -2x

Combine like terms: 31 + -9 = 22
22 + 3x + -2x + -5x2 = 9 + 2x + -9 + -2x

Combine like terms: 3x + -2x = 1x
22 + 1x + -5x2 = 9 + 2x + -9 + -2x

Reorder the terms:
22 + 1x + -5x2 = 9 + -9 + 2x + -2x

Combine like terms: 9 + -9 = 0
22 + 1x + -5x2 = 0 + 2x + -2x
22 + 1x + -5x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
22 + 1x + -5x2 = 0

Factor a trinomial.
(11 + -5x)(2 + x) = 0


Subproblem 1
Set the factor '(11 + -5x)' equal to zero and attempt to solve:

Simplifying
11 + -5x = 0

Solving
11 + -5x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -5x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -5x = 0 + -11
-5x = 0 + -11

Combine like terms: 0 + -11 = -11
-5x = -11

Divide each side by '-5'.
x = 2.2

Simplifying
x = 2.2

Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {2.2, -2}

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