x(5x+1)=3x(4x-1)

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Solution for x(5x+1)=3x(4x-1) equation: 


Simplifying
x(5x + 1) = 3x(4x + -1)

Reorder the terms:
x(1 + 5x) = 3x(4x + -1)
(1 * x + 5x * x) = 3x(4x + -1)
(1x + 5x2) = 3x(4x + -1)

Reorder the terms:
1x + 5x2 = 3x(-1 + 4x)
1x + 5x2 = (-1 * 3x + 4x * 3x)
1x + 5x2 = (-3x + 12x2)

Solving
1x + 5x2 = -3x + 12x2

Solving for variable 'x'.

Reorder the terms:
1x + 3x + 5x2 + -12x2 = -3x + 12x2 + 3x + -12x2

Combine like terms: 1x + 3x = 4x
4x + 5x2 + -12x2 = -3x + 12x2 + 3x + -12x2

Combine like terms: 5x2 + -12x2 = -7x2
4x + -7x2 = -3x + 12x2 + 3x + -12x2

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

Combine like terms: -3x + 3x = 0
4x + -7x2 = 0 + 12x2 + -12x2
4x + -7x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
4x + -7x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(4 + -7x) = 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 '(4 + -7x)' equal to zero and attempt to solve:

Simplifying
4 + -7x = 0

Solving
4 + -7x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -7x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7x = 0 + -4
-7x = 0 + -4

Combine like terms: 0 + -4 = -4
-7x = -4

Divide each side by '-7'.
x = 0.5714285714

Simplifying
x = 0.5714285714
Solution
x = {0, 0.5714285714}

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