(3x-1)(x+4)=x^2-3x-4

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Solution for (3x-1)(x+4)=x^2-3x-4 equation: 


Simplifying
(3x + -1)(x + 4) = x2 + -3x + -4

Reorder the terms:
(-1 + 3x)(x + 4) = x2 + -3x + -4

Reorder the terms:
(-1 + 3x)(4 + x) = x2 + -3x + -4

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

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

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

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

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

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

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

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

Solving
11x + 3x2 = -3x + x2

Solving for variable 'x'.

Reorder the terms:
11x + 3x + 3x2 + -1x2 = -3x + x2 + 3x + -1x2

Combine like terms: 11x + 3x = 14x
14x + 3x2 + -1x2 = -3x + x2 + 3x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
14x + 2x2 = -3x + x2 + 3x + -1x2

Reorder the terms:
14x + 2x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
14x + 2x2 = 0 + x2 + -1x2
14x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(7 + x) = 0

Ignore the factor 2.

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 '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {0, -7}

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