(2x+1)(2x+1)=10x-1

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Solution for (2x+1)(2x+1)=10x-1 equation: 


Simplifying
(2x + 1)(2x + 1) = 10x + -1

Reorder the terms:
(1 + 2x)(2x + 1) = 10x + -1

Reorder the terms:
(1 + 2x)(1 + 2x) = 10x + -1

Multiply (1 + 2x) * (1 + 2x)
(1(1 + 2x) + 2x * (1 + 2x)) = 10x + -1
((1 * 1 + 2x * 1) + 2x * (1 + 2x)) = 10x + -1
((1 + 2x) + 2x * (1 + 2x)) = 10x + -1
(1 + 2x + (1 * 2x + 2x * 2x)) = 10x + -1
(1 + 2x + (2x + 4x2)) = 10x + -1

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

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

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

Solving for variable 'x'.

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

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

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

Reorder the terms:
2 + -6x + 4x2 = -1 + 1 + 10x + -10x

Combine like terms: -1 + 1 = 0
2 + -6x + 4x2 = 0 + 10x + -10x
2 + -6x + 4x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
2 + -6x + 4x2 = 0

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

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

Ignore the factor 2.

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 '(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 = {0.5, 1}

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