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

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


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

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

Reorder the terms:
12x + 2x2 = 3(-3 + x)
12x + 2x2 = (-3 * 3 + x * 3)
12x + 2x2 = (-9 + 3x)

Solving
12x + 2x2 = -9 + 3x

Solving for variable 'x'.

Reorder the terms:
9 + 12x + -3x + 2x2 = -9 + 3x + 9 + -3x

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

Reorder the terms:
9 + 9x + 2x2 = -9 + 9 + 3x + -3x

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

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

Factor a trinomial.
(3 + x)(3 + 2x) = 0


Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

Simplifying
x = -3

Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {-3, -1.5}

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