(2x+1)(x-4)=11

Solution for (2x+1)(x-4)=11 equation:

Simplifying
(2x + 1)(x + -4) = 11

Reorder the terms:
(1 + 2x)(x + -4) = 11

Reorder the terms:
(1 + 2x)(-4 + x) = 11

Multiply (1 + 2x) * (-4 + x)
(1(-4 + x) + 2x * (-4 + x)) = 11
((-4 * 1 + x * 1) + 2x * (-4 + x)) = 11
((-4 + 1x) + 2x * (-4 + x)) = 11
(-4 + 1x + (-4 * 2x + x * 2x)) = 11
(-4 + 1x + (-8x + 2x2)) = 11

Combine like terms: 1x + -8x = -7x
(-4 + -7x + 2x2) = 11

Solving
-4 + -7x + 2x2 = 11

Solving for variable 'x'.

Reorder the terms:
-4 + -11 + -7x + 2x2 = 11 + -11

Combine like terms: -4 + -11 = -15
-15 + -7x + 2x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-15 + -7x + 2x2 = 0

Factor a trinomial.
(-3 + -2x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5
Subproblem 2
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
Solution
x = {-1.5, 5}