(2x+1)(x-4)=x+86

Solution for (2x+1)(x-4)=x+86 equation:

Simplifying
(2x + 1)(x + -4) = x + 86

Reorder the terms:
(1 + 2x)(x + -4) = x + 86

Reorder the terms:
(1 + 2x)(-4 + x) = x + 86

Multiply (1 + 2x) * (-4 + x)
(1(-4 + x) + 2x * (-4 + x)) = x + 86
((-4 * 1 + x * 1) + 2x * (-4 + x)) = x + 86
((-4 + 1x) + 2x * (-4 + x)) = x + 86
(-4 + 1x + (-4 * 2x + x * 2x)) = x + 86
(-4 + 1x + (-8x + 2x2)) = x + 86

Combine like terms: 1x + -8x = -7x
(-4 + -7x + 2x2) = x + 86

Reorder the terms:
-4 + -7x + 2x2 = 86 + x

Solving
-4 + -7x + 2x2 = 86 + x

Solving for variable 'x'.

Reorder the terms:
-4 + -86 + -7x + -1x + 2x2 = 86 + x + -86 + -1x

Combine like terms: -4 + -86 = -90
-90 + -7x + -1x + 2x2 = 86 + x + -86 + -1x

Combine like terms: -7x + -1x = -8x
-90 + -8x + 2x2 = 86 + x + -86 + -1x

Reorder the terms:
-90 + -8x + 2x2 = 86 + -86 + x + -1x

Combine like terms: 86 + -86 = 0
-90 + -8x + 2x2 = 0 + x + -1x
-90 + -8x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-90 + -8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + -4x + x2) = 0

Factor a trinomial.
2((-5 + -1x)(9 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-5, 9}