-4x^2=64-32x

Solution for -4x^2=64-32x equation:

Simplifying
-4x2 = 64 + -32x

Solving
-4x2 = 64 + -32x

Solving for variable 'x'.

Reorder the terms:
-64 + 32x + -4x2 = 64 + -32x + -64 + 32x

Reorder the terms:
-64 + 32x + -4x2 = 64 + -64 + -32x + 32x

Combine like terms: 64 + -64 = 0
-64 + 32x + -4x2 = 0 + -32x + 32x
-64 + 32x + -4x2 = -32x + 32x

Combine like terms: -32x + 32x = 0
-64 + 32x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-16 + 8x + -1x2) = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 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 + x = 0 + 4

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

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

Simplifying
x = 4
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {4, 4}