40=12+64x-16x^2

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Solution for 40=12+64x-16x^2 equation: 


Simplifying
40 = 12 + 64x + -16x2

Solving
40 = 12 + 64x + -16x2

Solving for variable 'x'.

Combine like terms: 40 + -12 = 28
28 + -64x + 16x2 = 12 + 64x + -16x2 + -12 + -64x + 16x2

Reorder the terms:
28 + -64x + 16x2 = 12 + -12 + 64x + -64x + -16x2 + 16x2

Combine like terms: 12 + -12 = 0
28 + -64x + 16x2 = 0 + 64x + -64x + -16x2 + 16x2
28 + -64x + 16x2 = 64x + -64x + -16x2 + 16x2

Combine like terms: 64x + -64x = 0
28 + -64x + 16x2 = 0 + -16x2 + 16x2
28 + -64x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
28 + -64x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + -16x + 4x2) = 0

Factor a trinomial.
4((1 + -2x)(7 + -2x)) = 0

Ignore the factor 4.

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {0.5, 3.5}

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