4x^2-78=5x^2+19x

Solution for 4x^2-78=5x^2+19x equation:

Simplifying
4x2 + -78 = 5x2 + 19x

Reorder the terms:
-78 + 4x2 = 5x2 + 19x

Reorder the terms:
-78 + 4x2 = 19x + 5x2

Solving
-78 + 4x2 = 19x + 5x2

Solving for variable 'x'.

Reorder the terms:
-78 + -19x + 4x2 + -5x2 = 19x + 5x2 + -19x + -5x2

Combine like terms: 4x2 + -5x2 = -1x2
-78 + -19x + -1x2 = 19x + 5x2 + -19x + -5x2

Reorder the terms:
-78 + -19x + -1x2 = 19x + -19x + 5x2 + -5x2

Combine like terms: 19x + -19x = 0
-78 + -19x + -1x2 = 0 + 5x2 + -5x2
-78 + -19x + -1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-78 + -19x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(78 + 19x + x2) = 0

Factor a trinomial.
-1((13 + x)(6 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(13 + x)' equal to zero and attempt to solve:

Simplifying
13 + x = 0

Solving
13 + x = 0

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

Add '-13' to each side of the equation.
13 + -13 + x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + x = 0 + -13
x = 0 + -13

Combine like terms: 0 + -13 = -13
x = -13

Simplifying
x = -13
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 = {-13, -6}