4x^2+92x+480=49x^2+238+289

Solution for 4x^2+92x+480=49x^2+238+289 equation:

Simplifying
4x2 + 92x + 480 = 49x2 + 238 + 289

Reorder the terms:
480 + 92x + 4x2 = 49x2 + 238 + 289

Reorder the terms:
480 + 92x + 4x2 = 238 + 289 + 49x2

Combine like terms: 238 + 289 = 527
480 + 92x + 4x2 = 527 + 49x2

Solving
480 + 92x + 4x2 = 527 + 49x2

Solving for variable 'x'.

Reorder the terms:
480 + -527 + 92x + 4x2 + -49x2 = 527 + 49x2 + -527 + -49x2

Combine like terms: 480 + -527 = -47
-47 + 92x + 4x2 + -49x2 = 527 + 49x2 + -527 + -49x2

Combine like terms: 4x2 + -49x2 = -45x2
-47 + 92x + -45x2 = 527 + 49x2 + -527 + -49x2

Reorder the terms:
-47 + 92x + -45x2 = 527 + -527 + 49x2 + -49x2

Combine like terms: 527 + -527 = 0
-47 + 92x + -45x2 = 0 + 49x2 + -49x2
-47 + 92x + -45x2 = 49x2 + -49x2

Combine like terms: 49x2 + -49x2 = 0
-47 + 92x + -45x2 = 0

Factor a trinomial.
(-47 + 45x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-47 + 45x)' equal to zero and attempt to solve:

Simplifying
-47 + 45x = 0

Solving
-47 + 45x = 0

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

Add '47' to each side of the equation.
-47 + 47 + 45x = 0 + 47

Combine like terms: -47 + 47 = 0
0 + 45x = 0 + 47
45x = 0 + 47

Combine like terms: 0 + 47 = 47
45x = 47

Divide each side by '45'.
x = 1.044444444

Simplifying
x = 1.044444444
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {1.044444444, 1}