x(9x+50)=35-3x(1+3x)

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Solution for x(9x+50)=35-3x(1+3x) equation:


Simplifying
x(9x + 50) = 35 + -3x(1 + 3x)

Reorder the terms:
x(50 + 9x) = 35 + -3x(1 + 3x)
(50 * x + 9x * x) = 35 + -3x(1 + 3x)
(50x + 9x2) = 35 + -3x(1 + 3x)
50x + 9x2 = 35 + (1 * -3x + 3x * -3x)
50x + 9x2 = 35 + (-3x + -9x2)

Solving
50x + 9x2 = 35 + -3x + -9x2

Solving for variable 'x'.

Reorder the terms:
-35 + 50x + 3x + 9x2 + 9x2 = 35 + -3x + -9x2 + -35 + 3x + 9x2

Combine like terms: 50x + 3x = 53x
-35 + 53x + 9x2 + 9x2 = 35 + -3x + -9x2 + -35 + 3x + 9x2

Combine like terms: 9x2 + 9x2 = 18x2
-35 + 53x + 18x2 = 35 + -3x + -9x2 + -35 + 3x + 9x2

Reorder the terms:
-35 + 53x + 18x2 = 35 + -35 + -3x + 3x + -9x2 + 9x2

Combine like terms: 35 + -35 = 0
-35 + 53x + 18x2 = 0 + -3x + 3x + -9x2 + 9x2
-35 + 53x + 18x2 = -3x + 3x + -9x2 + 9x2

Combine like terms: -3x + 3x = 0
-35 + 53x + 18x2 = 0 + -9x2 + 9x2
-35 + 53x + 18x2 = -9x2 + 9x2

Combine like terms: -9x2 + 9x2 = 0
-35 + 53x + 18x2 = 0

Factor a trinomial.
(-7 + -2x)(5 + -9x) = 0


Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 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 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

Subproblem 2
Set the factor '(5 + -9x)' equal to zero and attempt to solve:

Simplifying
5 + -9x = 0

Solving
5 + -9x = 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 + -9x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -9x = 0 + -5
-9x = 0 + -5

Combine like terms: 0 + -5 = -5
-9x = -5

Divide each side by '-9'.
x = 0.5555555556

Simplifying
x = 0.5555555556
Solution
x = {-3.5, 0.5555555556}

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