x(5x+10)=2x^2-13x+8

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Solution for x(5x+10)=2x^2-13x+8 equation: 


Simplifying
x(5x + 10) = 2x2 + -13x + 8

Reorder the terms:
x(10 + 5x) = 2x2 + -13x + 8
(10 * x + 5x * x) = 2x2 + -13x + 8
(10x + 5x2) = 2x2 + -13x + 8

Reorder the terms:
10x + 5x2 = 8 + -13x + 2x2

Solving
10x + 5x2 = 8 + -13x + 2x2

Solving for variable 'x'.

Reorder the terms:
-8 + 10x + 13x + 5x2 + -2x2 = 8 + -13x + 2x2 + -8 + 13x + -2x2

Combine like terms: 10x + 13x = 23x
-8 + 23x + 5x2 + -2x2 = 8 + -13x + 2x2 + -8 + 13x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-8 + 23x + 3x2 = 8 + -13x + 2x2 + -8 + 13x + -2x2

Reorder the terms:
-8 + 23x + 3x2 = 8 + -8 + -13x + 13x + 2x2 + -2x2

Combine like terms: 8 + -8 = 0
-8 + 23x + 3x2 = 0 + -13x + 13x + 2x2 + -2x2
-8 + 23x + 3x2 = -13x + 13x + 2x2 + -2x2

Combine like terms: -13x + 13x = 0
-8 + 23x + 3x2 = 0 + 2x2 + -2x2
-8 + 23x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-8 + 23x + 3x2 = 0

Factor a trinomial.
(-8 + -1x)(1 + -3x) = 0


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-8, 0.3333333333}

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