3x^2+45=-24x

Solution for 3x^2+45=-24x equation:

Simplifying
3x2 + 45 = -24x

Reorder the terms:
45 + 3x2 = -24x

Solving
45 + 3x2 = -24x

Solving for variable 'x'.

Reorder the terms:
45 + 24x + 3x2 = -24x + 24x

Combine like terms: -24x + 24x = 0
45 + 24x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(15 + 8x + x2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

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

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

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

Simplifying
x = -5
Subproblem 2
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
Solution
x = {-5, -3}