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

Solution for 4(5x+1)(x+3)=0 equation:

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

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

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

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

Combine like terms: 1x + 15x = 16x
4(3 + 16x + 5x2) = 0
(3 * 4 + 16x * 4 + 5x2 * 4) = 0
(12 + 64x + 20x2) = 0

Solving
12 + 64x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 16x + 5x2) = 0

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

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + 5x)' equal to zero and attempt to solve:

Simplifying
1 + 5x = 0

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

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

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

Divide each side by '5'.
x = -0.2

Simplifying
x = -0.2
Solution
x = {-3, -0.2}