x(5x+1)=2x^2-18x+40

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Solution for x(5x+1)=2x^2-18x+40 equation: 


Simplifying
x(5x + 1) = 2x2 + -18x + 40

Reorder the terms:
x(1 + 5x) = 2x2 + -18x + 40
(1 * x + 5x * x) = 2x2 + -18x + 40
(1x + 5x2) = 2x2 + -18x + 40

Reorder the terms:
1x + 5x2 = 40 + -18x + 2x2

Solving
1x + 5x2 = 40 + -18x + 2x2

Solving for variable 'x'.

Reorder the terms:
-40 + 1x + 18x + 5x2 + -2x2 = 40 + -18x + 2x2 + -40 + 18x + -2x2

Combine like terms: 1x + 18x = 19x
-40 + 19x + 5x2 + -2x2 = 40 + -18x + 2x2 + -40 + 18x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-40 + 19x + 3x2 = 40 + -18x + 2x2 + -40 + 18x + -2x2

Reorder the terms:
-40 + 19x + 3x2 = 40 + -40 + -18x + 18x + 2x2 + -2x2

Combine like terms: 40 + -40 = 0
-40 + 19x + 3x2 = 0 + -18x + 18x + 2x2 + -2x2
-40 + 19x + 3x2 = -18x + 18x + 2x2 + -2x2

Combine like terms: -18x + 18x = 0
-40 + 19x + 3x2 = 0 + 2x2 + -2x2
-40 + 19x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-40 + 19x + 3x2 = 0

Factor a trinomial.
(-8 + -1x)(5 + -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 '(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 = {-8, 1.666666667}

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