x(4x-1)+2(2x-1)=20

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Solution for x(4x-1)+2(2x-1)=20 equation: 


Simplifying
x(4x + -1) + 2(2x + -1) = 20

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

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

Reorder the terms:
-2 + -1x + 4x + 4x2 = 20

Combine like terms: -1x + 4x = 3x
-2 + 3x + 4x2 = 20

Solving
-2 + 3x + 4x2 = 20

Solving for variable 'x'.

Reorder the terms:
-2 + -20 + 3x + 4x2 = 20 + -20

Combine like terms: -2 + -20 = -22
-22 + 3x + 4x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-22 + 3x + 4x2 = 0

Factor a trinomial.
(-11 + -4x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-11 + -4x)' equal to zero and attempt to solve:

Simplifying
-11 + -4x = 0

Solving
-11 + -4x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -4x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -4x = 0 + 11
-4x = 0 + 11

Combine like terms: 0 + 11 = 11
-4x = 11

Divide each side by '-4'.
x = -2.75

Simplifying
x = -2.75

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-2.75, 2}

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