4x^2-114=5x^2+25x

Solution for 4x^2-114=5x^2+25x equation:

Simplifying
4x2 + -114 = 5x2 + 25x

Reorder the terms:
-114 + 4x2 = 5x2 + 25x

Reorder the terms:
-114 + 4x2 = 25x + 5x2

Solving
-114 + 4x2 = 25x + 5x2

Solving for variable 'x'.

Reorder the terms:
-114 + -25x + 4x2 + -5x2 = 25x + 5x2 + -25x + -5x2

Combine like terms: 4x2 + -5x2 = -1x2
-114 + -25x + -1x2 = 25x + 5x2 + -25x + -5x2

Reorder the terms:
-114 + -25x + -1x2 = 25x + -25x + 5x2 + -5x2

Combine like terms: 25x + -25x = 0
-114 + -25x + -1x2 = 0 + 5x2 + -5x2
-114 + -25x + -1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-114 + -25x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(114 + 25x + x2) = 0

Factor a trinomial.
-1((19 + x)(6 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(19 + x)' equal to zero and attempt to solve:

Simplifying
19 + x = 0

Solving
19 + x = 0

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

Add '-19' to each side of the equation.
19 + -19 + x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + x = 0 + -19
x = 0 + -19

Combine like terms: 0 + -19 = -19
x = -19

Simplifying
x = -19
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 = {-19, -6}