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

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

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

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

Multiply (3 + x) * (5 + -1x)
4(3(5 + -1x) + x(5 + -1x)) = 0
4((5 * 3 + -1x * 3) + x(5 + -1x)) = 0
4((15 + -3x) + x(5 + -1x)) = 0
4(15 + -3x + (5 * x + -1x * x)) = 0
4(15 + -3x + (5x + -1x2)) = 0

Combine like terms: -3x + 5x = 2x
4(15 + 2x + -1x2) = 0
(15 * 4 + 2x * 4 + -1x2 * 4) = 0
(60 + 8x + -4x2) = 0

Solving
60 + 8x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(15 + 2x + -1x2) = 0

Factor a trinomial.
4((5 + -1x)(3 + x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

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

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3
Solution
x = {5, -3}