4x(x+4)+x=6(1-x)

Solution for 4x(x+4)+x=6(1-x) equation:

Simplifying
4x(x + 4) + x = 6(1 + -1x)

Reorder the terms:
4x(4 + x) + x = 6(1 + -1x)
(4 * 4x + x * 4x) + x = 6(1 + -1x)
(16x + 4x2) + x = 6(1 + -1x)

Reorder the terms:
16x + x + 4x2 = 6(1 + -1x)

Combine like terms: 16x + x = 17x
17x + 4x2 = 6(1 + -1x)
17x + 4x2 = (1 * 6 + -1x * 6)
17x + 4x2 = (6 + -6x)

Solving
17x + 4x2 = 6 + -6x

Solving for variable 'x'.

Reorder the terms:
-6 + 17x + 6x + 4x2 = 6 + -6x + -6 + 6x

Combine like terms: 17x + 6x = 23x
-6 + 23x + 4x2 = 6 + -6x + -6 + 6x

Reorder the terms:
-6 + 23x + 4x2 = 6 + -6 + -6x + 6x

Combine like terms: 6 + -6 = 0
-6 + 23x + 4x2 = 0 + -6x + 6x
-6 + 23x + 4x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-6 + 23x + 4x2 = 0

Factor a trinomial.
(-6 + -1x)(1 + -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 '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {-6, 0.25}