(6-3x)(8+3x)=48

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Solution for (6-3x)(8+3x)=48 equation: 


Simplifying
(6 + -3x)(8 + 3x) = 48

Multiply (6 + -3x) * (8 + 3x)
(6(8 + 3x) + -3x * (8 + 3x)) = 48
((8 * 6 + 3x * 6) + -3x * (8 + 3x)) = 48
((48 + 18x) + -3x * (8 + 3x)) = 48
(48 + 18x + (8 * -3x + 3x * -3x)) = 48
(48 + 18x + (-24x + -9x2)) = 48

Combine like terms: 18x + -24x = -6x
(48 + -6x + -9x2) = 48

Add '-48' to each side of the equation.
48 + -6x + -48 + -9x2 = 48 + -48

Reorder the terms:
48 + -48 + -6x + -9x2 = 48 + -48

Combine like terms: 48 + -48 = 0
0 + -6x + -9x2 = 48 + -48
-6x + -9x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-6x + -9x2 = 0

Solving
-6x + -9x2 = 0

Solving for variable 'x'.

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

Ignore the factor -3.

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 '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

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

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

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

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

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {0, -0.6666666667}

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