5x(2+9x)-(2+9x)15=0

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Solution for 5x(2+9x)-(2+9x)15=0 equation: 


Simplifying
5x(2 + 9x) + -1(2 + 9x) * 15 = 0
(2 * 5x + 9x * 5x) + -1(2 + 9x) * 15 = 0
(10x + 45x2) + -1(2 + 9x) * 15 = 0

Reorder the terms for easier multiplication:
10x + 45x2 + -1 * 15(2 + 9x) = 0

Multiply -1 * 15
10x + 45x2 + -15(2 + 9x) = 0
10x + 45x2 + (2 * -15 + 9x * -15) = 0
10x + 45x2 + (-30 + -135x) = 0

Reorder the terms:
-30 + 10x + -135x + 45x2 = 0

Combine like terms: 10x + -135x = -125x
-30 + -125x + 45x2 = 0

Solving
-30 + -125x + 45x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-6 + -25x + 9x2) = 0

Factor a trinomial.
5((-2 + -9x)(3 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-2 + -9x)' equal to zero and attempt to solve:

Simplifying
-2 + -9x = 0

Solving
-2 + -9x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -9x = 0 + 2

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

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

Divide each side by '-9'.
x = -0.2222222222

Simplifying
x = -0.2222222222

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 = {-0.2222222222, 3}

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