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

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


Simplifying
x(2x + -3) + 2x(x + 6) = 0

Reorder the terms:
x(-3 + 2x) + 2x(x + 6) = 0
(-3 * x + 2x * x) + 2x(x + 6) = 0
(-3x + 2x2) + 2x(x + 6) = 0

Reorder the terms:
-3x + 2x2 + 2x(6 + x) = 0
-3x + 2x2 + (6 * 2x + x * 2x) = 0
-3x + 2x2 + (12x + 2x2) = 0

Reorder the terms:
-3x + 12x + 2x2 + 2x2 = 0

Combine like terms: -3x + 12x = 9x
9x + 2x2 + 2x2 = 0

Combine like terms: 2x2 + 2x2 = 4x2
9x + 4x2 = 0

Solving
9x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(9 + 4x) = 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 '(9 + 4x)' equal to zero and attempt to solve:

Simplifying
9 + 4x = 0

Solving
9 + 4x = 0

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

Add '-9' to each side of the equation.
9 + -9 + 4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 4x = 0 + -9
4x = 0 + -9

Combine like terms: 0 + -9 = -9
4x = -9

Divide each side by '4'.
x = -2.25

Simplifying
x = -2.25
Solution
x = {0, -2.25}

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