(2x+1)(x-4)=1586

Solution for (2x+1)(x-4)=1586 equation:

Simplifying
(2x + 1)(x + -4) = 1586

Reorder the terms:
(1 + 2x)(x + -4) = 1586

Reorder the terms:
(1 + 2x)(-4 + x) = 1586

Multiply (1 + 2x) * (-4 + x)
(1(-4 + x) + 2x * (-4 + x)) = 1586
((-4 * 1 + x * 1) + 2x * (-4 + x)) = 1586
((-4 + 1x) + 2x * (-4 + x)) = 1586
(-4 + 1x + (-4 * 2x + x * 2x)) = 1586
(-4 + 1x + (-8x + 2x2)) = 1586

Combine like terms: 1x + -8x = -7x
(-4 + -7x + 2x2) = 1586

Solving
-4 + -7x + 2x2 = 1586

Solving for variable 'x'.

Reorder the terms:
-4 + -1586 + -7x + 2x2 = 1586 + -1586

Combine like terms: -4 + -1586 = -1590
-1590 + -7x + 2x2 = 1586 + -1586

Combine like terms: 1586 + -1586 = 0
-1590 + -7x + 2x2 = 0

Factor a trinomial.
(-53 + -2x)(30 + -1x) = 0

Subproblem 1
Set the factor '(-53 + -2x)' equal to zero and attempt to solve:

Simplifying
-53 + -2x = 0

Solving
-53 + -2x = 0

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

Add '53' to each side of the equation.
-53 + 53 + -2x = 0 + 53

Combine like terms: -53 + 53 = 0
0 + -2x = 0 + 53
-2x = 0 + 53

Combine like terms: 0 + 53 = 53
-2x = 53

Divide each side by '-2'.
x = -26.5

Simplifying
x = -26.5
Subproblem 2
Set the factor '(30 + -1x)' equal to zero and attempt to solve:

Simplifying
30 + -1x = 0

Solving
30 + -1x = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1x = 0 + -30
-1x = 0 + -30

Combine like terms: 0 + -30 = -30
-1x = -30

Divide each side by '-1'.
x = 30

Simplifying
x = 30
Solution
x = {-26.5, 30}