5x+9=16x^2-24x+9

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Solution for 5x+9=16x^2-24x+9 equation: 


Simplifying
5x + 9 = 16x2 + -24x + 9

Reorder the terms:
9 + 5x = 16x2 + -24x + 9

Reorder the terms:
9 + 5x = 9 + -24x + 16x2

Add '-9' to each side of the equation.
9 + -9 + 5x = 9 + -24x + -9 + 16x2

Combine like terms: 9 + -9 = 0
0 + 5x = 9 + -24x + -9 + 16x2
5x = 9 + -24x + -9 + 16x2

Reorder the terms:
5x = 9 + -9 + -24x + 16x2

Combine like terms: 9 + -9 = 0
5x = 0 + -24x + 16x2
5x = -24x + 16x2

Solving
5x = -24x + 16x2

Solving for variable 'x'.

Combine like terms: 5x + 24x = 29x
29x + -16x2 = -24x + 16x2 + 24x + -16x2

Reorder the terms:
29x + -16x2 = -24x + 24x + 16x2 + -16x2

Combine like terms: -24x + 24x = 0
29x + -16x2 = 0 + 16x2 + -16x2
29x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
29x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(29 + -16x) = 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 '(29 + -16x)' equal to zero and attempt to solve:

Simplifying
29 + -16x = 0

Solving
29 + -16x = 0

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

Add '-29' to each side of the equation.
29 + -29 + -16x = 0 + -29

Combine like terms: 29 + -29 = 0
0 + -16x = 0 + -29
-16x = 0 + -29

Combine like terms: 0 + -29 = -29
-16x = -29

Divide each side by '-16'.
x = 1.8125

Simplifying
x = 1.8125
Solution
x = {0, 1.8125}

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