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

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

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

Reorder the terms:
2(3 + x)(2x + 4) + 3(x + -3) = 0

Reorder the terms:
2(3 + x)(4 + 2x) + 3(x + -3) = 0

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

Combine like terms: 6x + 4x = 10x
2(12 + 10x + 2x2) + 3(x + -3) = 0
(12 * 2 + 10x * 2 + 2x2 * 2) + 3(x + -3) = 0
(24 + 20x + 4x2) + 3(x + -3) = 0

Reorder the terms:
24 + 20x + 4x2 + 3(-3 + x) = 0
24 + 20x + 4x2 + (-3 * 3 + x * 3) = 0
24 + 20x + 4x2 + (-9 + 3x) = 0

Reorder the terms:
24 + -9 + 20x + 3x + 4x2 = 0

Combine like terms: 24 + -9 = 15
15 + 20x + 3x + 4x2 = 0

Combine like terms: 20x + 3x = 23x
15 + 23x + 4x2 = 0

Solving
15 + 23x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + x)(3 + 4x) = 0

Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(3 + 4x)' equal to zero and attempt to solve:

Simplifying
3 + 4x = 0

Solving
3 + 4x = 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 + 4x = 0 + -3

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

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

Divide each side by '4'.
x = -0.75

Simplifying
x = -0.75
Solution
x = {-5, -0.75}