x(x+3)+2x(x-2)=6x(x+4)

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Solution for x(x+3)+2x(x-2)=6x(x+4) equation: 


Simplifying
x(x + 3) + 2x(x + -2) = 6x(x + 4)

Reorder the terms:
x(3 + x) + 2x(x + -2) = 6x(x + 4)
(3 * x + x * x) + 2x(x + -2) = 6x(x + 4)
(3x + x2) + 2x(x + -2) = 6x(x + 4)

Reorder the terms:
3x + x2 + 2x(-2 + x) = 6x(x + 4)
3x + x2 + (-2 * 2x + x * 2x) = 6x(x + 4)
3x + x2 + (-4x + 2x2) = 6x(x + 4)

Reorder the terms:
3x + -4x + x2 + 2x2 = 6x(x + 4)

Combine like terms: 3x + -4x = -1x
-1x + x2 + 2x2 = 6x(x + 4)

Combine like terms: x2 + 2x2 = 3x2
-1x + 3x2 = 6x(x + 4)

Reorder the terms:
-1x + 3x2 = 6x(4 + x)
-1x + 3x2 = (4 * 6x + x * 6x)
-1x + 3x2 = (24x + 6x2)

Solving
-1x + 3x2 = 24x + 6x2

Solving for variable 'x'.

Reorder the terms:
-1x + -24x + 3x2 + -6x2 = 24x + 6x2 + -24x + -6x2

Combine like terms: -1x + -24x = -25x
-25x + 3x2 + -6x2 = 24x + 6x2 + -24x + -6x2

Combine like terms: 3x2 + -6x2 = -3x2
-25x + -3x2 = 24x + 6x2 + -24x + -6x2

Reorder the terms:
-25x + -3x2 = 24x + -24x + 6x2 + -6x2

Combine like terms: 24x + -24x = 0
-25x + -3x2 = 0 + 6x2 + -6x2
-25x + -3x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-25x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(25 + 3x) = 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 '(25 + 3x)' equal to zero and attempt to solve:

Simplifying
25 + 3x = 0

Solving
25 + 3x = 0

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

Add '-25' to each side of the equation.
25 + -25 + 3x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 3x = 0 + -25
3x = 0 + -25

Combine like terms: 0 + -25 = -25
3x = -25

Divide each side by '3'.
x = -8.333333333

Simplifying
x = -8.333333333
Solution
x = {0, -8.333333333}

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