9(x+5)=2x(x-7)+5(x+9)

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Solution for 9(x+5)=2x(x-7)+5(x+9) equation: 


Simplifying
9(x + 5) = 2x(x + -7) + 5(x + 9)

Reorder the terms:
9(5 + x) = 2x(x + -7) + 5(x + 9)
(5 * 9 + x * 9) = 2x(x + -7) + 5(x + 9)
(45 + 9x) = 2x(x + -7) + 5(x + 9)

Reorder the terms:
45 + 9x = 2x(-7 + x) + 5(x + 9)
45 + 9x = (-7 * 2x + x * 2x) + 5(x + 9)
45 + 9x = (-14x + 2x2) + 5(x + 9)

Reorder the terms:
45 + 9x = -14x + 2x2 + 5(9 + x)
45 + 9x = -14x + 2x2 + (9 * 5 + x * 5)
45 + 9x = -14x + 2x2 + (45 + 5x)

Reorder the terms:
45 + 9x = 45 + -14x + 5x + 2x2

Combine like terms: -14x + 5x = -9x
45 + 9x = 45 + -9x + 2x2

Add '-45' to each side of the equation.
45 + -45 + 9x = 45 + -9x + -45 + 2x2

Combine like terms: 45 + -45 = 0
0 + 9x = 45 + -9x + -45 + 2x2
9x = 45 + -9x + -45 + 2x2

Reorder the terms:
9x = 45 + -45 + -9x + 2x2

Combine like terms: 45 + -45 = 0
9x = 0 + -9x + 2x2
9x = -9x + 2x2

Solving
9x = -9x + 2x2

Solving for variable 'x'.

Combine like terms: 9x + 9x = 18x
18x + -2x2 = -9x + 2x2 + 9x + -2x2

Reorder the terms:
18x + -2x2 = -9x + 9x + 2x2 + -2x2

Combine like terms: -9x + 9x = 0
18x + -2x2 = 0 + 2x2 + -2x2
18x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
18x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(9 + -1x) = 0

Ignore the factor 2.

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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 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 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {0, 9}

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