4x^2+160x+1600=784

Solution for 4x^2+160x+1600=784 equation:

Simplifying
4x2 + 160x + 1600 = 784

Reorder the terms:
1600 + 160x + 4x2 = 784

Solving
1600 + 160x + 4x2 = 784

Solving for variable 'x'.

Reorder the terms:
1600 + -784 + 160x + 4x2 = 784 + -784

Combine like terms: 1600 + -784 = 816
816 + 160x + 4x2 = 784 + -784

Combine like terms: 784 + -784 = 0
816 + 160x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(204 + 40x + x2) = 0

Factor a trinomial.
4((34 + x)(6 + x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(34 + x)' equal to zero and attempt to solve:

Simplifying
34 + x = 0

Solving
34 + x = 0

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

Add '-34' to each side of the equation.
34 + -34 + x = 0 + -34

Combine like terms: 34 + -34 = 0
0 + x = 0 + -34
x = 0 + -34

Combine like terms: 0 + -34 = -34
x = -34

Simplifying
x = -34
Subproblem 2
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
Solution
x = {-34, -6}