12x+x=-3x(4-x)

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Solution for 12x+x=-3x(4-x) equation:


Simplifying
12x + x = -3x(4 + -1x)

Combine like terms: 12x + x = 13x
13x = -3x(4 + -1x)
13x = (4 * -3x + -1x * -3x)
13x = (-12x + 3x2)

Solving
13x = -12x + 3x2

Solving for variable 'x'.

Combine like terms: 13x + 12x = 25x
25x + -3x2 = -12x + 3x2 + 12x + -3x2

Reorder the terms:
25x + -3x2 = -12x + 12x + 3x2 + -3x2

Combine like terms: -12x + 12x = 0
25x + -3x2 = 0 + 3x2 + -3x2
25x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
25x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(25 + -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 '(25 + -3x)' equal to zero and attempt to solve:

Simplifying
25 + -3x = 0

Solving
25 + -3x = 0

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

Add '-25' to each side of the equation.
25 + -25 + -3x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -3x = 0 + -25
-3x = 0 + -25

Combine like terms: 0 + -25 = -25
-3x = -25

Divide each side by '-3'.
x = 8.333333333

Simplifying
x = 8.333333333
Solution
x = {0, 8.333333333}

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