4x^2-80x=-400

Solution for 4x^2-80x=-400 equation:

Simplifying
4x2 + -80x = -400

Reorder the terms:
-80x + 4x2 = -400

Solving
-80x + 4x2 = -400

Solving for variable 'x'.

Reorder the terms:
400 + -80x + 4x2 = -400 + 400

Combine like terms: -400 + 400 = 0
400 + -80x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(100 + -20x + x2) = 0

Factor a trinomial.
4((10 + -1x)(10 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {10, 10}