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

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

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

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

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

Multiply (1 + 3x) * (-3 + x)
4(1(-3 + x) + 3x * (-3 + x)) = 0
4((-3 * 1 + x * 1) + 3x * (-3 + x)) = 0
4((-3 + 1x) + 3x * (-3 + x)) = 0
4(-3 + 1x + (-3 * 3x + x * 3x)) = 0
4(-3 + 1x + (-9x + 3x2)) = 0

Combine like terms: 1x + -9x = -8x
4(-3 + -8x + 3x2) = 0
(-3 * 4 + -8x * 4 + 3x2 * 4) = 0
(-12 + -32x + 12x2) = 0

Solving
-12 + -32x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + -8x + 3x2) = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve:

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Subproblem 2
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
Solution
x = {-0.3333333333, 3}