5x(4x-19)=x^2-114

Solution for 5x(4x-19)=x^2-114 equation:

Simplifying
5x(4x + -19) = x2 + -114

Reorder the terms:
5x(-19 + 4x) = x2 + -114
(-19 * 5x + 4x * 5x) = x2 + -114
(-95x + 20x2) = x2 + -114

Reorder the terms:
-95x + 20x2 = -114 + x2

Solving
-95x + 20x2 = -114 + x2

Solving for variable 'x'.

Reorder the terms:
114 + -95x + 20x2 + -1x2 = -114 + x2 + 114 + -1x2

Combine like terms: 20x2 + -1x2 = 19x2
114 + -95x + 19x2 = -114 + x2 + 114 + -1x2

Reorder the terms:
114 + -95x + 19x2 = -114 + 114 + x2 + -1x2

Combine like terms: -114 + 114 = 0
114 + -95x + 19x2 = 0 + x2 + -1x2
114 + -95x + 19x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
114 + -95x + 19x2 = 0

Factor out the Greatest Common Factor (GCF), '19'.
19(6 + -5x + x2) = 0

Factor a trinomial.
19((2 + -1x)(3 + -1x)) = 0

Ignore the factor 19.
Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {2, 3}