4x^2+32x+49=1

Solution for 4x^2+32x+49=1 equation:

Simplifying
4x2 + 32x + 49 = 1

Reorder the terms:
49 + 32x + 4x2 = 1

Solving
49 + 32x + 4x2 = 1

Solving for variable 'x'.

Reorder the terms:
49 + -1 + 32x + 4x2 = 1 + -1

Combine like terms: 49 + -1 = 48
48 + 32x + 4x2 = 1 + -1

Combine like terms: 1 + -1 = 0
48 + 32x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(12 + 8x + x2) = 0

Factor a trinomial.
4((6 + x)(2 + x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
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 = {-6, -2}