(8x^2+2x-6)-(5x^2-3x+2)=0

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Solution for (8x^2+2x-6)-(5x^2-3x+2)=0 equation: 


Simplifying
(8x2 + 2x + -6) + -1(5x2 + -3x + 2) = 0

Reorder the terms:
(-6 + 2x + 8x2) + -1(5x2 + -3x + 2) = 0

Remove parenthesis around (-6 + 2x + 8x2)
-6 + 2x + 8x2 + -1(5x2 + -3x + 2) = 0

Reorder the terms:
-6 + 2x + 8x2 + -1(2 + -3x + 5x2) = 0
-6 + 2x + 8x2 + (2 * -1 + -3x * -1 + 5x2 * -1) = 0
-6 + 2x + 8x2 + (-2 + 3x + -5x2) = 0

Reorder the terms:
-6 + -2 + 2x + 3x + 8x2 + -5x2 = 0

Combine like terms: -6 + -2 = -8
-8 + 2x + 3x + 8x2 + -5x2 = 0

Combine like terms: 2x + 3x = 5x
-8 + 5x + 8x2 + -5x2 = 0

Combine like terms: 8x2 + -5x2 = 3x2
-8 + 5x + 3x2 = 0

Solving
-8 + 5x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -3x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-8 + -3x)' equal to zero and attempt to solve:

Simplifying
-8 + -3x = 0

Solving
-8 + -3x = 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 + -3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3x = 0 + 8
-3x = 0 + 8

Combine like terms: 0 + 8 = 8
-3x = 8

Divide each side by '-3'.
x = -2.666666667

Simplifying
x = -2.666666667

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-2.666666667, 1}

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