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

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


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

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

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

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

Combine like terms: -2x + 4x = 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.
(-3 + -2x)(5 + -4x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-1.5, 1.25}

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