7x=3x(x-4)

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Solution for 7x=3x(x-4) equation: 


Simplifying
7x = 3x(x + -4)

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

Solving
7x = -12x + 3x2

Solving for variable 'x'.

Combine like terms: 7x + 12x = 19x
19x + -3x2 = -12x + 3x2 + 12x + -3x2

Reorder the terms:
19x + -3x2 = -12x + 12x + 3x2 + -3x2

Combine like terms: -12x + 12x = 0
19x + -3x2 = 0 + 3x2 + -3x2
19x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
19x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(19 + -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 '(19 + -3x)' equal to zero and attempt to solve:

Simplifying
19 + -3x = 0

Solving
19 + -3x = 0

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

Add '-19' to each side of the equation.
19 + -19 + -3x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -3x = 0 + -19
-3x = 0 + -19

Combine like terms: 0 + -19 = -19
-3x = -19

Divide each side by '-3'.
x = 6.333333333

Simplifying
x = 6.333333333
Solution
x = {0, 6.333333333}

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