51x(x-3)+6=5x-9

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Solution for 51x(x-3)+6=5x-9 equation:


Simplifying
51x(x + -3) + 6 = 5x + -9

Reorder the terms:
51x(-3 + x) + 6 = 5x + -9
(-3 * 51x + x * 51x) + 6 = 5x + -9
(-153x + 51x2) + 6 = 5x + -9

Reorder the terms:
6 + -153x + 51x2 = 5x + -9

Reorder the terms:
6 + -153x + 51x2 = -9 + 5x

Solving
6 + -153x + 51x2 = -9 + 5x

Solving for variable 'x'.

Reorder the terms:
6 + 9 + -153x + -5x + 51x2 = -9 + 5x + 9 + -5x

Combine like terms: 6 + 9 = 15
15 + -153x + -5x + 51x2 = -9 + 5x + 9 + -5x

Combine like terms: -153x + -5x = -158x
15 + -158x + 51x2 = -9 + 5x + 9 + -5x

Reorder the terms:
15 + -158x + 51x2 = -9 + 9 + 5x + -5x

Combine like terms: -9 + 9 = 0
15 + -158x + 51x2 = 0 + 5x + -5x
15 + -158x + 51x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
15 + -158x + 51x2 = 0

Factor a trinomial.
(5 + -51x)(3 + -1x) = 0


Subproblem 1
Set the factor '(5 + -51x)' equal to zero and attempt to solve:

Simplifying
5 + -51x = 0

Solving
5 + -51x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -51x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -51x = 0 + -5
-51x = 0 + -5

Combine like terms: 0 + -5 = -5
-51x = -5

Divide each side by '-51'.
x = 0.09803921569

Simplifying
x = 0.09803921569

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.09803921569, 3}

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