8X^2=-32X+40

Solution for 8X^2=-32X+40 equation:

Simplifying
8X2 = -32X + 40

Reorder the terms:
8X2 = 40 + -32X

Solving
8X2 = 40 + -32X

Solving for variable 'X'.

Reorder the terms:
-40 + 32X + 8X2 = 40 + -32X + -40 + 32X

Reorder the terms:
-40 + 32X + 8X2 = 40 + -40 + -32X + 32X

Combine like terms: 40 + -40 = 0
-40 + 32X + 8X2 = 0 + -32X + 32X
-40 + 32X + 8X2 = -32X + 32X

Combine like terms: -32X + 32X = 0
-40 + 32X + 8X2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-5 + 4X + X2) = 0

Factor a trinomial.
8((-5 + -1X)(1 + -1X)) = 0

Ignore the factor 8.
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 '(1 + -1X)' equal to zero and attempt to solve:

Simplifying
1 + -1X = 0

Solving
1 + -1X = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1X = 0 + -1
-1X = 0 + -1

Combine like terms: 0 + -1 = -1
-1X = -1

Divide each side by '-1'.
X = 1

Simplifying
X = 1
Solution
X = {-5, 1}