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

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

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

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

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

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

Solving
2x + x2 = -3 + 6x

Solving for variable 'x'.

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

Combine like terms: 2x + -6x = -4x
3 + -4x + x2 = -3 + 6x + 3 + -6x

Reorder the terms:
3 + -4x + x2 = -3 + 3 + 6x + -6x

Combine like terms: -3 + 3 = 0
3 + -4x + x2 = 0 + 6x + -6x
3 + -4x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
3 + -4x + x2 = 0

Factor a trinomial.
(1 + -1x)(3 + -1x) = 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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1, 3}