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

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


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

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

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

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

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

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

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

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

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

Solving for variable 'x'.

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

Combine like terms: -2 + -9 = -11
-11 + -5x + -3x + 3x2 = 9 + 3x + -9 + -3x

Combine like terms: -5x + -3x = -8x
-11 + -8x + 3x2 = 9 + 3x + -9 + -3x

Reorder the terms:
-11 + -8x + 3x2 = 9 + -9 + 3x + -3x

Combine like terms: 9 + -9 = 0
-11 + -8x + 3x2 = 0 + 3x + -3x
-11 + -8x + 3x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-11 + -8x + 3x2 = 0

Factor a trinomial.
(-1 + -1x)(11 + -3x) = 0


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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1x = 0 + 1

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(11 + -3x)' equal to zero and attempt to solve:

Simplifying
11 + -3x = 0

Solving
11 + -3x = 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 + -3x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3x = 0 + -11
-3x = 0 + -11

Combine like terms: 0 + -11 = -11
-3x = -11

Divide each side by '-3'.
x = 3.666666667

Simplifying
x = 3.666666667
Solution
x = {-1, 3.666666667}

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