(2x-1)(4x+1)=14

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Solution for (2x-1)(4x+1)=14 equation: 


Simplifying
(2x + -1)(4x + 1) = 14

Reorder the terms:
(-1 + 2x)(4x + 1) = 14

Reorder the terms:
(-1 + 2x)(1 + 4x) = 14

Multiply (-1 + 2x) * (1 + 4x)
(-1(1 + 4x) + 2x * (1 + 4x)) = 14
((1 * -1 + 4x * -1) + 2x * (1 + 4x)) = 14
((-1 + -4x) + 2x * (1 + 4x)) = 14
(-1 + -4x + (1 * 2x + 4x * 2x)) = 14
(-1 + -4x + (2x + 8x2)) = 14

Combine like terms: -4x + 2x = -2x
(-1 + -2x + 8x2) = 14

Solving
-1 + -2x + 8x2 = 14

Solving for variable 'x'.

Reorder the terms:
-1 + -14 + -2x + 8x2 = 14 + -14

Combine like terms: -1 + -14 = -15
-15 + -2x + 8x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-15 + -2x + 8x2 = 0

Factor a trinomial.
(-5 + -4x)(3 + -2x) = 0


Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve:

Simplifying
-5 + -4x = 0

Solving
-5 + -4x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -4x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4x = 0 + 5
-4x = 0 + 5

Combine like terms: 0 + 5 = 5
-4x = 5

Divide each side by '-4'.
x = -1.25

Simplifying
x = -1.25

Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-1.25, 1.5}

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