5x-4=3x(x+4)

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


Simplifying
5x + -4 = 3x(x + 4)

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

Reorder the terms:
-4 + 5x = 3x(4 + x)
-4 + 5x = (4 * 3x + x * 3x)
-4 + 5x = (12x + 3x2)

Solving
-4 + 5x = 12x + 3x2

Solving for variable 'x'.

Combine like terms: 5x + -12x = -7x
-4 + -7x + -3x2 = 12x + 3x2 + -12x + -3x2

Reorder the terms:
-4 + -7x + -3x2 = 12x + -12x + 3x2 + -3x2

Combine like terms: 12x + -12x = 0
-4 + -7x + -3x2 = 0 + 3x2 + -3x2
-4 + -7x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-4 + -7x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 7x + 3x2) = 0

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

Ignore the factor -1.

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

Simplifying
4 + 3x = 0

Solving
4 + 3x = 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 + 3x = 0 + -4

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

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

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {-1.333333333, -1}

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