x(5x+11)=2x^2-2x+10

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Solution for x(5x+11)=2x^2-2x+10 equation: 


Simplifying
x(5x + 11) = 2x2 + -2x + 10

Reorder the terms:
x(11 + 5x) = 2x2 + -2x + 10
(11 * x + 5x * x) = 2x2 + -2x + 10
(11x + 5x2) = 2x2 + -2x + 10

Reorder the terms:
11x + 5x2 = 10 + -2x + 2x2

Solving
11x + 5x2 = 10 + -2x + 2x2

Solving for variable 'x'.

Reorder the terms:
-10 + 11x + 2x + 5x2 + -2x2 = 10 + -2x + 2x2 + -10 + 2x + -2x2

Combine like terms: 11x + 2x = 13x
-10 + 13x + 5x2 + -2x2 = 10 + -2x + 2x2 + -10 + 2x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-10 + 13x + 3x2 = 10 + -2x + 2x2 + -10 + 2x + -2x2

Reorder the terms:
-10 + 13x + 3x2 = 10 + -10 + -2x + 2x + 2x2 + -2x2

Combine like terms: 10 + -10 = 0
-10 + 13x + 3x2 = 0 + -2x + 2x + 2x2 + -2x2
-10 + 13x + 3x2 = -2x + 2x + 2x2 + -2x2

Combine like terms: -2x + 2x = 0
-10 + 13x + 3x2 = 0 + 2x2 + -2x2
-10 + 13x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-10 + 13x + 3x2 = 0

Factor a trinomial.
(-5 + -1x)(2 + -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 '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-5, 0.6666666667}

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