1.5x(6-2x)=3x-9

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Solution for 1.5x(6-2x)=3x-9 equation: 


Simplifying
1.5x(6 + -2x) = 3x + -9
(6 * 1.5x + -2x * 1.5x) = 3x + -9
(9x + -3x2) = 3x + -9

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

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

Solving for variable 'x'.

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

Combine like terms: 9x + -3x = 6x
9 + 6x + -3x2 = -9 + 3x + 9 + -3x

Reorder the terms:
9 + 6x + -3x2 = -9 + 9 + 3x + -3x

Combine like terms: -9 + 9 = 0
9 + 6x + -3x2 = 0 + 3x + -3x
9 + 6x + -3x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
9 + 6x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 2x + -1x2) = 0

Factor a trinomial.
3((3 + -1x)(1 + x)) = 0

Ignore the factor 3.

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {3, -1}

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