2x+3+2x(2x+3)=6x+9

Solution for 2x+3+2x(2x+3)=6x+9 equation:

Simplifying
2x + 3 + 2x(2x + 3) = 6x + 9

Reorder the terms:
2x + 3 + 2x(3 + 2x) = 6x + 9
2x + 3 + (3 * 2x + 2x * 2x) = 6x + 9
2x + 3 + (6x + 4x2) = 6x + 9

Reorder the terms:
3 + 2x + 6x + 4x2 = 6x + 9

Combine like terms: 2x + 6x = 8x
3 + 8x + 4x2 = 6x + 9

Reorder the terms:
3 + 8x + 4x2 = 9 + 6x

Solving
3 + 8x + 4x2 = 9 + 6x

Solving for variable 'x'.

Reorder the terms:
3 + -9 + 8x + -6x + 4x2 = 9 + 6x + -9 + -6x

Combine like terms: 3 + -9 = -6
-6 + 8x + -6x + 4x2 = 9 + 6x + -9 + -6x

Combine like terms: 8x + -6x = 2x
-6 + 2x + 4x2 = 9 + 6x + -9 + -6x

Reorder the terms:
-6 + 2x + 4x2 = 9 + -9 + 6x + -6x

Combine like terms: 9 + -9 = 0
-6 + 2x + 4x2 = 0 + 6x + -6x
-6 + 2x + 4x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-6 + 2x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + x + 2x2) = 0

Factor a trinomial.
2((-3 + -2x)(1 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
x = {-1.5, 1}