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

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


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

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

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

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

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

Reorder the terms:
6 + -1x + 2x2 = 6 + x

Add '-6' to each side of the equation.
6 + -1x + -6 + 2x2 = 6 + -6 + x

Reorder the terms:
6 + -6 + -1x + 2x2 = 6 + -6 + x

Combine like terms: 6 + -6 = 0
0 + -1x + 2x2 = 6 + -6 + x
-1x + 2x2 = 6 + -6 + x

Combine like terms: 6 + -6 = 0
-1x + 2x2 = 0 + x
-1x + 2x2 = x

Solving
-1x + 2x2 = x

Solving for variable 'x'.

Reorder the terms:
-1x + -1x + 2x2 = x + -1x

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

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

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-1 + x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 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 + x = 0 + 1

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

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

Simplifying
x = 1
Solution
x = {0, 1}

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