2(x+4)5(3-x)=

Solution for 2(x+4)5(3-x)= equation:

Simplifying
2(x + 4) * 5(3 + -1x) = 0

Reorder the terms:
2(4 + x) * 5(3 + -1x) = 0

Reorder the terms for easier multiplication:
2 * 5(4 + x)(3 + -1x) = 0

Multiply 2 * 5
10(4 + x)(3 + -1x) = 0

Multiply (4 + x) * (3 + -1x)
10(4(3 + -1x) + x(3 + -1x)) = 0
10((3 * 4 + -1x * 4) + x(3 + -1x)) = 0
10((12 + -4x) + x(3 + -1x)) = 0
10(12 + -4x + (3 * x + -1x * x)) = 0
10(12 + -4x + (3x + -1x2)) = 0

Combine like terms: -4x + 3x = -1x
10(12 + -1x + -1x2) = 0
(12 * 10 + -1x * 10 + -1x2 * 10) = 0
(120 + -10x + -10x2) = 0

Solving
120 + -10x + -10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(12 + -1x + -1x2) = 0

Factor a trinomial.
10((3 + -1x)(4 + x)) = 0

Ignore the factor 10.
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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

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

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

Simplifying
x = -4
Solution
x = {3, -4}