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

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


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

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

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

Solving for variable 'x'.

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

Combine like terms: 3x + 5x = 8x
8x + 12x2 + -1x2 = -5x + 1x2 + 5x + -1x2

Combine like terms: 12x2 + -1x2 = 11x2
8x + 11x2 = -5x + 1x2 + 5x + -1x2

Reorder the terms:
8x + 11x2 = -5x + 5x + 1x2 + -1x2

Combine like terms: -5x + 5x = 0
8x + 11x2 = 0 + 1x2 + -1x2
8x + 11x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
8x + 11x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(8 + 11x) = 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 + 11x)' equal to zero and attempt to solve:

Simplifying
8 + 11x = 0

Solving
8 + 11x = 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 + 11x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 11x = 0 + -8
11x = 0 + -8

Combine like terms: 0 + -8 = -8
11x = -8

Divide each side by '11'.
x = -0.7272727273

Simplifying
x = -0.7272727273
Solution
x = {0, -0.7272727273}

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