x(7x+14)=2x^2-22x+32

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Solution for x(7x+14)=2x^2-22x+32 equation: 


Simplifying
x(7x + 14) = 2x2 + -22x + 32

Reorder the terms:
x(14 + 7x) = 2x2 + -22x + 32
(14 * x + 7x * x) = 2x2 + -22x + 32
(14x + 7x2) = 2x2 + -22x + 32

Reorder the terms:
14x + 7x2 = 32 + -22x + 2x2

Solving
14x + 7x2 = 32 + -22x + 2x2

Solving for variable 'x'.

Reorder the terms:
-32 + 14x + 22x + 7x2 + -2x2 = 32 + -22x + 2x2 + -32 + 22x + -2x2

Combine like terms: 14x + 22x = 36x
-32 + 36x + 7x2 + -2x2 = 32 + -22x + 2x2 + -32 + 22x + -2x2

Combine like terms: 7x2 + -2x2 = 5x2
-32 + 36x + 5x2 = 32 + -22x + 2x2 + -32 + 22x + -2x2

Reorder the terms:
-32 + 36x + 5x2 = 32 + -32 + -22x + 22x + 2x2 + -2x2

Combine like terms: 32 + -32 = 0
-32 + 36x + 5x2 = 0 + -22x + 22x + 2x2 + -2x2
-32 + 36x + 5x2 = -22x + 22x + 2x2 + -2x2

Combine like terms: -22x + 22x = 0
-32 + 36x + 5x2 = 0 + 2x2 + -2x2
-32 + 36x + 5x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-32 + 36x + 5x2 = 0

Factor a trinomial.
(-8 + -1x)(4 + -5x) = 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 '(4 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

Solving
4 + -5x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x = 0 + -4
-5x = 0 + -4

Combine like terms: 0 + -4 = -4
-5x = -4

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8
Solution
x = {-8, 0.8}

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