10x-1=4x^2+4x+1

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Solution for 10x-1=4x^2+4x+1 equation: 


Simplifying
10x + -1 = 4x2 + 4x + 1

Reorder the terms:
-1 + 10x = 4x2 + 4x + 1

Reorder the terms:
-1 + 10x = 1 + 4x + 4x2

Solving
-1 + 10x = 1 + 4x + 4x2

Solving for variable 'x'.

Reorder the terms:
-1 + -1 + 10x + -4x + -4x2 = 1 + 4x + 4x2 + -1 + -4x + -4x2

Combine like terms: -1 + -1 = -2
-2 + 10x + -4x + -4x2 = 1 + 4x + 4x2 + -1 + -4x + -4x2

Combine like terms: 10x + -4x = 6x
-2 + 6x + -4x2 = 1 + 4x + 4x2 + -1 + -4x + -4x2

Reorder the terms:
-2 + 6x + -4x2 = 1 + -1 + 4x + -4x + 4x2 + -4x2

Combine like terms: 1 + -1 = 0
-2 + 6x + -4x2 = 0 + 4x + -4x + 4x2 + -4x2
-2 + 6x + -4x2 = 4x + -4x + 4x2 + -4x2

Combine like terms: 4x + -4x = 0
-2 + 6x + -4x2 = 0 + 4x2 + -4x2
-2 + 6x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-2 + 6x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 3x + -2x2) = 0

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

Ignore the factor 2.

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

Simplifying
-1 + x = 0

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

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

Combine like terms: 0 + 1 = 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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