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

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


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

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

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

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

Solving for variable 'x'.

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

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

Combine like terms: 3x2 + -4x2 = -1x2
8x + -1x2 = -4x + 4x2 + 4x + -4x2

Reorder the terms:
8x + -1x2 = -4x + 4x + 4x2 + -4x2

Combine like terms: -4x + 4x = 0
8x + -1x2 = 0 + 4x2 + -4x2
8x + -1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
8x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(8 + -1x) = 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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {0, 8}

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