4x^2-34=5x^2+19x

Solution for 4x^2-34=5x^2+19x equation:

Simplifying
4x2 + -34 = 5x2 + 19x

Reorder the terms:
-34 + 4x2 = 5x2 + 19x

Reorder the terms:
-34 + 4x2 = 19x + 5x2

Solving
-34 + 4x2 = 19x + 5x2

Solving for variable 'x'.

Reorder the terms:
-34 + -19x + 4x2 + -5x2 = 19x + 5x2 + -19x + -5x2

Combine like terms: 4x2 + -5x2 = -1x2
-34 + -19x + -1x2 = 19x + 5x2 + -19x + -5x2

Reorder the terms:
-34 + -19x + -1x2 = 19x + -19x + 5x2 + -5x2

Combine like terms: 19x + -19x = 0
-34 + -19x + -1x2 = 0 + 5x2 + -5x2
-34 + -19x + -1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-34 + -19x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(34 + 19x + x2) = 0

Factor a trinomial.
-1((17 + x)(2 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(17 + x)' equal to zero and attempt to solve:

Simplifying
17 + x = 0

Solving
17 + x = 0

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

Add '-17' to each side of the equation.
17 + -17 + x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + x = 0 + -17
x = 0 + -17

Combine like terms: 0 + -17 = -17
x = -17

Simplifying
x = -17
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-17, -2}