10=4x^2-2x+8

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Solution for 10=4x^2-2x+8 equation: 


Simplifying
10 = 4x2 + -2x + 8

Reorder the terms:
10 = 8 + -2x + 4x2

Solving
10 = 8 + -2x + 4x2

Solving for variable 'x'.

Combine like terms: 10 + -8 = 2
2 + 2x + -4x2 = 8 + -2x + 4x2 + -8 + 2x + -4x2

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

Combine like terms: 8 + -8 = 0
2 + 2x + -4x2 = 0 + -2x + 2x + 4x2 + -4x2
2 + 2x + -4x2 = -2x + 2x + 4x2 + -4x2

Combine like terms: -2x + 2x = 0
2 + 2x + -4x2 = 0 + 4x2 + -4x2
2 + 2x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
2 + 2x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + x + -2x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
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
Solution
x = {1, -0.5}

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