x(7x+1)=2x^2-16x+40

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Solution for x(7x+1)=2x^2-16x+40 equation: 


Simplifying
x(7x + 1) = 2x2 + -16x + 40

Reorder the terms:
x(1 + 7x) = 2x2 + -16x + 40
(1 * x + 7x * x) = 2x2 + -16x + 40
(1x + 7x2) = 2x2 + -16x + 40

Reorder the terms:
1x + 7x2 = 40 + -16x + 2x2

Solving
1x + 7x2 = 40 + -16x + 2x2

Solving for variable 'x'.

Reorder the terms:
-40 + 1x + 16x + 7x2 + -2x2 = 40 + -16x + 2x2 + -40 + 16x + -2x2

Combine like terms: 1x + 16x = 17x
-40 + 17x + 7x2 + -2x2 = 40 + -16x + 2x2 + -40 + 16x + -2x2

Combine like terms: 7x2 + -2x2 = 5x2
-40 + 17x + 5x2 = 40 + -16x + 2x2 + -40 + 16x + -2x2

Reorder the terms:
-40 + 17x + 5x2 = 40 + -40 + -16x + 16x + 2x2 + -2x2

Combine like terms: 40 + -40 = 0
-40 + 17x + 5x2 = 0 + -16x + 16x + 2x2 + -2x2
-40 + 17x + 5x2 = -16x + 16x + 2x2 + -2x2

Combine like terms: -16x + 16x = 0
-40 + 17x + 5x2 = 0 + 2x2 + -2x2
-40 + 17x + 5x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-40 + 17x + 5x2 = 0

Factor a trinomial.
(-5 + -1x)(8 + -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 '(8 + -5x)' equal to zero and attempt to solve:

Simplifying
8 + -5x = 0

Solving
8 + -5x = 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 + -5x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5x = 0 + -8
-5x = 0 + -8

Combine like terms: 0 + -8 = -8
-5x = -8

Divide each side by '-5'.
x = 1.6

Simplifying
x = 1.6
Solution
x = {-5, 1.6}

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