(3x+5)(9-x)=15(x+3)

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Solution for (3x+5)(9-x)=15(x+3) equation: 


Simplifying
(3x + 5)(9 + -1x) = 15(x + 3)

Reorder the terms:
(5 + 3x)(9 + -1x) = 15(x + 3)

Multiply (5 + 3x) * (9 + -1x)
(5(9 + -1x) + 3x * (9 + -1x)) = 15(x + 3)
((9 * 5 + -1x * 5) + 3x * (9 + -1x)) = 15(x + 3)
((45 + -5x) + 3x * (9 + -1x)) = 15(x + 3)
(45 + -5x + (9 * 3x + -1x * 3x)) = 15(x + 3)
(45 + -5x + (27x + -3x2)) = 15(x + 3)

Combine like terms: -5x + 27x = 22x
(45 + 22x + -3x2) = 15(x + 3)

Reorder the terms:
45 + 22x + -3x2 = 15(3 + x)
45 + 22x + -3x2 = (3 * 15 + x * 15)
45 + 22x + -3x2 = (45 + 15x)

Add '-45' to each side of the equation.
45 + 22x + -45 + -3x2 = 45 + -45 + 15x

Reorder the terms:
45 + -45 + 22x + -3x2 = 45 + -45 + 15x

Combine like terms: 45 + -45 = 0
0 + 22x + -3x2 = 45 + -45 + 15x
22x + -3x2 = 45 + -45 + 15x

Combine like terms: 45 + -45 = 0
22x + -3x2 = 0 + 15x
22x + -3x2 = 15x

Solving
22x + -3x2 = 15x

Solving for variable 'x'.

Reorder the terms:
22x + -15x + -3x2 = 15x + -15x

Combine like terms: 22x + -15x = 7x
7x + -3x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
7x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(7 + -3x) = 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 '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {0, 2.333333333}

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