(2x+1)(x-4)=-7

Solution for (2x+1)(x-4)=-7 equation:

Simplifying
(2x + 1)(x + -4) = -7

Reorder the terms:
(1 + 2x)(x + -4) = -7

Reorder the terms:
(1 + 2x)(-4 + x) = -7

Multiply (1 + 2x) * (-4 + x)
(1(-4 + x) + 2x * (-4 + x)) = -7
((-4 * 1 + x * 1) + 2x * (-4 + x)) = -7
((-4 + 1x) + 2x * (-4 + x)) = -7
(-4 + 1x + (-4 * 2x + x * 2x)) = -7
(-4 + 1x + (-8x + 2x2)) = -7

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

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

Solving for variable 'x'.

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

Combine like terms: -4 + 7 = 3
3 + -7x + 2x2 = -7 + 7

Combine like terms: -7 + 7 = 0
3 + -7x + 2x2 = 0

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

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.5, 3}