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

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


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

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

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

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

Combine like terms: 1x + -12x = -11x
4(-4 + -11x + 3x2) = 0
(-4 * 4 + -11x * 4 + 3x2 * 4) = 0
(-16 + -44x + 12x2) = 0

Solving
-16 + -44x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + -11x + 3x2) = 0

Factor a trinomial.
4((-1 + -3x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-0.3333333333, 4}

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