4(5x-1)+x(4x+1)=13+1

Solution for 4(5x-1)+x(4x+1)=13+1 equation:

Simplifying
4(5x + -1) + x(4x + 1) = 13 + 1

Reorder the terms:
4(-1 + 5x) + x(4x + 1) = 13 + 1
(-1 * 4 + 5x * 4) + x(4x + 1) = 13 + 1
(-4 + 20x) + x(4x + 1) = 13 + 1

Reorder the terms:
-4 + 20x + x(1 + 4x) = 13 + 1
-4 + 20x + (1 * x + 4x * x) = 13 + 1
-4 + 20x + (1x + 4x2) = 13 + 1

Combine like terms: 20x + 1x = 21x
-4 + 21x + 4x2 = 13 + 1

Combine like terms: 13 + 1 = 14
-4 + 21x + 4x2 = 14

Solving
-4 + 21x + 4x2 = 14

Solving for variable 'x'.

Reorder the terms:
-4 + -14 + 21x + 4x2 = 14 + -14

Combine like terms: -4 + -14 = -18
-18 + 21x + 4x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-18 + 21x + 4x2 = 0

Factor a trinomial.
(-6 + -1x)(3 + -4x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-6, 0.75}