2x(x+1)=5-7x

Solution for 2x(x+1)=5-7x equation:

Simplifying
2x(x + 1) = 5 + -7x

Reorder the terms:
2x(1 + x) = 5 + -7x
(1 * 2x + x * 2x) = 5 + -7x
(2x + 2x2) = 5 + -7x

Solving
2x + 2x2 = 5 + -7x

Solving for variable 'x'.

Reorder the terms:
-5 + 2x + 7x + 2x2 = 5 + -7x + -5 + 7x

Combine like terms: 2x + 7x = 9x
-5 + 9x + 2x2 = 5 + -7x + -5 + 7x

Reorder the terms:
-5 + 9x + 2x2 = 5 + -5 + -7x + 7x

Combine like terms: 5 + -5 = 0
-5 + 9x + 2x2 = 0 + -7x + 7x
-5 + 9x + 2x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
-5 + 9x + 2x2 = 0

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

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 '(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
Solution
x = {-5, 0.5}