(2x-1)(5x+2)=1

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Solution for (2x-1)(5x+2)=1 equation: 


Simplifying
(2x + -1)(5x + 2) = 1

Reorder the terms:
(-1 + 2x)(5x + 2) = 1

Reorder the terms:
(-1 + 2x)(2 + 5x) = 1

Multiply (-1 + 2x) * (2 + 5x)
(-1(2 + 5x) + 2x * (2 + 5x)) = 1
((2 * -1 + 5x * -1) + 2x * (2 + 5x)) = 1
((-2 + -5x) + 2x * (2 + 5x)) = 1
(-2 + -5x + (2 * 2x + 5x * 2x)) = 1
(-2 + -5x + (4x + 10x2)) = 1

Combine like terms: -5x + 4x = -1x
(-2 + -1x + 10x2) = 1

Solving
-2 + -1x + 10x2 = 1

Solving for variable 'x'.

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

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

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

Factor a trinomial.
(-1 + -2x)(3 + -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 '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5x = 0 + -3

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

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

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {-0.5, 0.6}

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