8x^2+4x-2=-x(2x-3)

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Solution for 8x^2+4x-2=-x(2x-3) equation: 


Simplifying
8x2 + 4x + -2 = -1x(2x + -3)

Reorder the terms:
-2 + 4x + 8x2 = -1x(2x + -3)

Reorder the terms:
-2 + 4x + 8x2 = -1x(-3 + 2x)
-2 + 4x + 8x2 = (-3 * -1x + 2x * -1x)
-2 + 4x + 8x2 = (3x + -2x2)

Solving
-2 + 4x + 8x2 = 3x + -2x2

Solving for variable 'x'.

Reorder the terms:
-2 + 4x + -3x + 8x2 + 2x2 = 3x + -2x2 + -3x + 2x2

Combine like terms: 4x + -3x = 1x
-2 + 1x + 8x2 + 2x2 = 3x + -2x2 + -3x + 2x2

Combine like terms: 8x2 + 2x2 = 10x2
-2 + 1x + 10x2 = 3x + -2x2 + -3x + 2x2

Reorder the terms:
-2 + 1x + 10x2 = 3x + -3x + -2x2 + 2x2

Combine like terms: 3x + -3x = 0
-2 + 1x + 10x2 = 0 + -2x2 + 2x2
-2 + 1x + 10x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-2 + 1x + 10x2 = 0

Factor a trinomial.
(-1 + -2x)(2 + -5x) = 0


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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 2
Set the factor '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {-0.5, 0.4}

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