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

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


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

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

Reorder the terms:
-4x + 2x2 = 3(3 + x)
-4x + 2x2 = (3 * 3 + x * 3)
-4x + 2x2 = (9 + 3x)

Solving
-4x + 2x2 = 9 + 3x

Solving for variable 'x'.

Reorder the terms:
-9 + -4x + -3x + 2x2 = 9 + 3x + -9 + -3x

Combine like terms: -4x + -3x = -7x
-9 + -7x + 2x2 = 9 + 3x + -9 + -3x

Reorder the terms:
-9 + -7x + 2x2 = 9 + -9 + 3x + -3x

Combine like terms: 9 + -9 = 0
-9 + -7x + 2x2 = 0 + 3x + -3x
-9 + -7x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-9 + -7x + 2x2 = 0

Factor a trinomial.
(-1 + -1x)(9 + -2x) = 0


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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1x = 0 + 1
-1x = 0 + 1

Combine like terms: 0 + 1 = 1
-1x = 1

Divide each side by '-1'.
x = -1

Simplifying
x = -1

Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 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 + -2x = 0 + -9

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

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

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {-1, 4.5}

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