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

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


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

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

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

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

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

Add '4' to each side of the equation.
-4 + -11x + 4 + 3x2 = -4 + 4

Reorder the terms:
-4 + 4 + -11x + 3x2 = -4 + 4

Combine like terms: -4 + 4 = 0
0 + -11x + 3x2 = -4 + 4
-11x + 3x2 = -4 + 4

Combine like terms: -4 + 4 = 0
-11x + 3x2 = 0

Solving
-11x + 3x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-11 + 3x)' equal to zero and attempt to solve:

Simplifying
-11 + 3x = 0

Solving
-11 + 3x = 0

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

Add '11' to each side of the equation.
-11 + 11 + 3x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 3x = 0 + 11
3x = 0 + 11

Combine like terms: 0 + 11 = 11
3x = 11

Divide each side by '3'.
x = 3.666666667

Simplifying
x = 3.666666667
Solution
x = {0, 3.666666667}

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