4x(x+3)-(x+3)2=

Solution for 4x(x+3)-(x+3)2= equation:

Simplifying
4x(x + 3) + -1(x + 3) * 2 = 0

Reorder the terms:
4x(3 + x) + -1(x + 3) * 2 = 0
(3 * 4x + x * 4x) + -1(x + 3) * 2 = 0
(12x + 4x2) + -1(x + 3) * 2 = 0

Reorder the terms:
12x + 4x2 + -1(3 + x) * 2 = 0

Reorder the terms for easier multiplication:
12x + 4x2 + -1 * 2(3 + x) = 0

Multiply -1 * 2
12x + 4x2 + -2(3 + x) = 0
12x + 4x2 + (3 * -2 + x * -2) = 0
12x + 4x2 + (-6 + -2x) = 0

Reorder the terms:
-6 + 12x + -2x + 4x2 = 0

Combine like terms: 12x + -2x = 10x
-6 + 10x + 4x2 = 0

Solving
-6 + 10x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 5x + 2x2) = 0

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

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-3, 0.5}