10x^2+18x+9=16x^2-24x+9

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Solution for 10x^2+18x+9=16x^2-24x+9 equation: 


Simplifying
10x2 + 18x + 9 = 16x2 + -24x + 9

Reorder the terms:
9 + 18x + 10x2 = 16x2 + -24x + 9

Reorder the terms:
9 + 18x + 10x2 = 9 + -24x + 16x2

Add '-9' to each side of the equation.
9 + 18x + -9 + 10x2 = 9 + -24x + -9 + 16x2

Reorder the terms:
9 + -9 + 18x + 10x2 = 9 + -24x + -9 + 16x2

Combine like terms: 9 + -9 = 0
0 + 18x + 10x2 = 9 + -24x + -9 + 16x2
18x + 10x2 = 9 + -24x + -9 + 16x2

Reorder the terms:
18x + 10x2 = 9 + -9 + -24x + 16x2

Combine like terms: 9 + -9 = 0
18x + 10x2 = 0 + -24x + 16x2
18x + 10x2 = -24x + 16x2

Solving
18x + 10x2 = -24x + 16x2

Solving for variable 'x'.

Reorder the terms:
18x + 24x + 10x2 + -16x2 = -24x + 16x2 + 24x + -16x2

Combine like terms: 18x + 24x = 42x
42x + 10x2 + -16x2 = -24x + 16x2 + 24x + -16x2

Combine like terms: 10x2 + -16x2 = -6x2
42x + -6x2 = -24x + 16x2 + 24x + -16x2

Reorder the terms:
42x + -6x2 = -24x + 24x + 16x2 + -16x2

Combine like terms: -24x + 24x = 0
42x + -6x2 = 0 + 16x2 + -16x2
42x + -6x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
42x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6x'.
6x(7 + -1x) = 0

Ignore the factor 6.

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

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {0, 7}

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