5x(4x-3)-(2x-1)=1

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Solution for 5x(4x-3)-(2x-1)=1 equation: 


Simplifying
5x(4x + -3) + -1(2x + -1) = 1

Reorder the terms:
5x(-3 + 4x) + -1(2x + -1) = 1
(-3 * 5x + 4x * 5x) + -1(2x + -1) = 1
(-15x + 20x2) + -1(2x + -1) = 1

Reorder the terms:
-15x + 20x2 + -1(-1 + 2x) = 1
-15x + 20x2 + (-1 * -1 + 2x * -1) = 1
-15x + 20x2 + (1 + -2x) = 1

Reorder the terms:
1 + -15x + -2x + 20x2 = 1

Combine like terms: -15x + -2x = -17x
1 + -17x + 20x2 = 1

Add '-1' to each side of the equation.
1 + -17x + -1 + 20x2 = 1 + -1

Reorder the terms:
1 + -1 + -17x + 20x2 = 1 + -1

Combine like terms: 1 + -1 = 0
0 + -17x + 20x2 = 1 + -1
-17x + 20x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-17x + 20x2 = 0

Solving
-17x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-17 + 20x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-17 + 20x)' equal to zero and attempt to solve:

Simplifying
-17 + 20x = 0

Solving
-17 + 20x = 0

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

Add '17' to each side of the equation.
-17 + 17 + 20x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 20x = 0 + 17
20x = 0 + 17

Combine like terms: 0 + 17 = 17
20x = 17

Divide each side by '20'.
x = 0.85

Simplifying
x = 0.85
Solution
x = {0, 0.85}

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