-10-5x^2=19x+2

Solution for -10-5x^2=19x+2 equation:

Simplifying
-10 + -5x2 = 19x + 2

Reorder the terms:
-10 + -5x2 = 2 + 19x

Solving
-10 + -5x2 = 2 + 19x

Solving for variable 'x'.

Reorder the terms:
-10 + -2 + -19x + -5x2 = 2 + 19x + -2 + -19x

Combine like terms: -10 + -2 = -12
-12 + -19x + -5x2 = 2 + 19x + -2 + -19x

Reorder the terms:
-12 + -19x + -5x2 = 2 + -2 + 19x + -19x

Combine like terms: 2 + -2 = 0
-12 + -19x + -5x2 = 0 + 19x + -19x
-12 + -19x + -5x2 = 19x + -19x

Combine like terms: 19x + -19x = 0
-12 + -19x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 19x + 5x2) = 0

Factor a trinomial.
-1((3 + x)(4 + 5x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Subproblem 2
Set the factor '(4 + 5x)' equal to zero and attempt to solve:

Simplifying
4 + 5x = 0

Solving
4 + 5x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5x = 0 + -4
5x = 0 + -4

Combine like terms: 0 + -4 = -4
5x = -4

Divide each side by '5'.
x = -0.8

Simplifying
x = -0.8
Solution
x = {-3, -0.8}