x(5x+1)=2x^2-9x+25

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Solution for x(5x+1)=2x^2-9x+25 equation: 


Simplifying
x(5x + 1) = 2x2 + -9x + 25

Reorder the terms:
x(1 + 5x) = 2x2 + -9x + 25
(1 * x + 5x * x) = 2x2 + -9x + 25
(1x + 5x2) = 2x2 + -9x + 25

Reorder the terms:
1x + 5x2 = 25 + -9x + 2x2

Solving
1x + 5x2 = 25 + -9x + 2x2

Solving for variable 'x'.

Reorder the terms:
-25 + 1x + 9x + 5x2 + -2x2 = 25 + -9x + 2x2 + -25 + 9x + -2x2

Combine like terms: 1x + 9x = 10x
-25 + 10x + 5x2 + -2x2 = 25 + -9x + 2x2 + -25 + 9x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-25 + 10x + 3x2 = 25 + -9x + 2x2 + -25 + 9x + -2x2

Reorder the terms:
-25 + 10x + 3x2 = 25 + -25 + -9x + 9x + 2x2 + -2x2

Combine like terms: 25 + -25 = 0
-25 + 10x + 3x2 = 0 + -9x + 9x + 2x2 + -2x2
-25 + 10x + 3x2 = -9x + 9x + 2x2 + -2x2

Combine like terms: -9x + 9x = 0
-25 + 10x + 3x2 = 0 + 2x2 + -2x2
-25 + 10x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-25 + 10x + 3x2 = 0

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


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

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {-5, 1.666666667}

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