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

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

Simplifying
2x2 + 6(x + 1) + -3x = 6

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

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

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

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

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

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

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

Solving
3x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(3 + 2x) = 0

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 '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {0, -1.5}