4x^2-66=5x^2+17x

Solution for 4x^2-66=5x^2+17x equation:

Simplifying
4x2 + -66 = 5x2 + 17x

Reorder the terms:
-66 + 4x2 = 5x2 + 17x

Reorder the terms:
-66 + 4x2 = 17x + 5x2

Solving
-66 + 4x2 = 17x + 5x2

Solving for variable 'x'.

Reorder the terms:
-66 + -17x + 4x2 + -5x2 = 17x + 5x2 + -17x + -5x2

Combine like terms: 4x2 + -5x2 = -1x2
-66 + -17x + -1x2 = 17x + 5x2 + -17x + -5x2

Reorder the terms:
-66 + -17x + -1x2 = 17x + -17x + 5x2 + -5x2

Combine like terms: 17x + -17x = 0
-66 + -17x + -1x2 = 0 + 5x2 + -5x2
-66 + -17x + -1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-66 + -17x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(66 + 17x + x2) = 0

Factor a trinomial.
-1((11 + x)(6 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(11 + x)' equal to zero and attempt to solve:

Simplifying
11 + x = 0

Solving
11 + x = 0

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

Add '-11' to each side of the equation.
11 + -11 + x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + x = 0 + -11
x = 0 + -11

Combine like terms: 0 + -11 = -11
x = -11

Simplifying
x = -11
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 = {-11, -6}