4x+2x^2+15=45

Solution for 4x+2x^2+15=45 equation:

Simplifying
4x + 2x2 + 15 = 45

Reorder the terms:
15 + 4x + 2x2 = 45

Solving
15 + 4x + 2x2 = 45

Solving for variable 'x'.

Reorder the terms:
15 + -45 + 4x + 2x2 = 45 + -45

Combine like terms: 15 + -45 = -30
-30 + 4x + 2x2 = 45 + -45

Combine like terms: 45 + -45 = 0
-30 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 2x + x2) = 0

Factor a trinomial.
2((-5 + -1x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
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 = {-5, 3}