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

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

Simplifying
1 + -4(2x + 1) = x2 + 4

Reorder the terms:
1 + -4(1 + 2x) = x2 + 4
1 + (1 * -4 + 2x * -4) = x2 + 4
1 + (-4 + -8x) = x2 + 4

Combine like terms: 1 + -4 = -3
-3 + -8x = x2 + 4

Reorder the terms:
-3 + -8x = 4 + x2

Solving
-3 + -8x = 4 + x2

Solving for variable 'x'.

Reorder the terms:
-3 + -4 + -8x + -1x2 = 4 + x2 + -4 + -1x2

Combine like terms: -3 + -4 = -7
-7 + -8x + -1x2 = 4 + x2 + -4 + -1x2

Reorder the terms:
-7 + -8x + -1x2 = 4 + -4 + x2 + -1x2

Combine like terms: 4 + -4 = 0
-7 + -8x + -1x2 = 0 + x2 + -1x2
-7 + -8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-7 + -8x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 8x + x2) = 0

Factor a trinomial.
-1((7 + x)(1 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {-7, -1}