x(7x+4)=2x^2-8x+32

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Solution for x(7x+4)=2x^2-8x+32 equation: 


Simplifying
x(7x + 4) = 2x2 + -8x + 32

Reorder the terms:
x(4 + 7x) = 2x2 + -8x + 32
(4 * x + 7x * x) = 2x2 + -8x + 32
(4x + 7x2) = 2x2 + -8x + 32

Reorder the terms:
4x + 7x2 = 32 + -8x + 2x2

Solving
4x + 7x2 = 32 + -8x + 2x2

Solving for variable 'x'.

Reorder the terms:
-32 + 4x + 8x + 7x2 + -2x2 = 32 + -8x + 2x2 + -32 + 8x + -2x2

Combine like terms: 4x + 8x = 12x
-32 + 12x + 7x2 + -2x2 = 32 + -8x + 2x2 + -32 + 8x + -2x2

Combine like terms: 7x2 + -2x2 = 5x2
-32 + 12x + 5x2 = 32 + -8x + 2x2 + -32 + 8x + -2x2

Reorder the terms:
-32 + 12x + 5x2 = 32 + -32 + -8x + 8x + 2x2 + -2x2

Combine like terms: 32 + -32 = 0
-32 + 12x + 5x2 = 0 + -8x + 8x + 2x2 + -2x2
-32 + 12x + 5x2 = -8x + 8x + 2x2 + -2x2

Combine like terms: -8x + 8x = 0
-32 + 12x + 5x2 = 0 + 2x2 + -2x2
-32 + 12x + 5x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-32 + 12x + 5x2 = 0

Factor a trinomial.
(-4 + -1x)(8 + -5x) = 0


Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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 = {-4, 1.6}

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