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

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


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

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

Multiply x * x
-3x + 3x2 = 4x2

Solving
-3x + 3x2 = 4x2

Solving for variable 'x'.

Combine like terms: 3x2 + -4x2 = -1x2
-3x + -1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-3x + -1x2 = 0

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

Ignore the factor -1.

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

Simplifying
x = -3
Solution
x = {0, -3}

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