-4(x+1)=x^2

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

Simplifying
-4(x + 1) = x2

Reorder the terms:
-4(1 + x) = x2
(1 * -4 + x * -4) = x2
(-4 + -4x) = x2

Solving
-4 + -4x = x2

Solving for variable 'x'.

Combine like terms: x2 + -1x2 = 0
-4 + -4x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 4x + x2) = 0

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

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2
Solution
x = {-2, -2}