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

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


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

Reorder the terms:
-3x(-1 + 3x) = 4x(-1x + 2)
(-1 * -3x + 3x * -3x) = 4x(-1x + 2)
(3x + -9x2) = 4x(-1x + 2)

Reorder the terms:
3x + -9x2 = 4x(2 + -1x)
3x + -9x2 = (2 * 4x + -1x * 4x)
3x + -9x2 = (8x + -4x2)

Solving
3x + -9x2 = 8x + -4x2

Solving for variable 'x'.

Reorder the terms:
3x + -8x + -9x2 + 4x2 = 8x + -4x2 + -8x + 4x2

Combine like terms: 3x + -8x = -5x
-5x + -9x2 + 4x2 = 8x + -4x2 + -8x + 4x2

Combine like terms: -9x2 + 4x2 = -5x2
-5x + -5x2 = 8x + -4x2 + -8x + 4x2

Reorder the terms:
-5x + -5x2 = 8x + -8x + -4x2 + 4x2

Combine like terms: 8x + -8x = 0
-5x + -5x2 = 0 + -4x2 + 4x2
-5x + -5x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-5x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '-5x'.
-5x(1 + x) = 0

Ignore the factor -5.

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 '(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 = {0, -1}

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