x(7x+13)=2x^2-11x+5

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Solution for x(7x+13)=2x^2-11x+5 equation: 


Simplifying
x(7x + 13) = 2x2 + -11x + 5

Reorder the terms:
x(13 + 7x) = 2x2 + -11x + 5
(13 * x + 7x * x) = 2x2 + -11x + 5
(13x + 7x2) = 2x2 + -11x + 5

Reorder the terms:
13x + 7x2 = 5 + -11x + 2x2

Solving
13x + 7x2 = 5 + -11x + 2x2

Solving for variable 'x'.

Reorder the terms:
-5 + 13x + 11x + 7x2 + -2x2 = 5 + -11x + 2x2 + -5 + 11x + -2x2

Combine like terms: 13x + 11x = 24x
-5 + 24x + 7x2 + -2x2 = 5 + -11x + 2x2 + -5 + 11x + -2x2

Combine like terms: 7x2 + -2x2 = 5x2
-5 + 24x + 5x2 = 5 + -11x + 2x2 + -5 + 11x + -2x2

Reorder the terms:
-5 + 24x + 5x2 = 5 + -5 + -11x + 11x + 2x2 + -2x2

Combine like terms: 5 + -5 = 0
-5 + 24x + 5x2 = 0 + -11x + 11x + 2x2 + -2x2
-5 + 24x + 5x2 = -11x + 11x + 2x2 + -2x2

Combine like terms: -11x + 11x = 0
-5 + 24x + 5x2 = 0 + 2x2 + -2x2
-5 + 24x + 5x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-5 + 24x + 5x2 = 0

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

Simplifying
1 + -5x = 0

Solving
1 + -5x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5x = 0 + -1

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

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

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2
Solution
x = {-5, 0.2}

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