-16x^2=16x+3

Solution for -16x^2=16x+3 equation:

Simplifying
-16x2 = 16x + 3

Reorder the terms:
-16x2 = 3 + 16x

Solving
-16x2 = 3 + 16x

Solving for variable 'x'.

Reorder the terms:
-3 + -16x + -16x2 = 3 + 16x + -3 + -16x

Reorder the terms:
-3 + -16x + -16x2 = 3 + -3 + 16x + -16x

Combine like terms: 3 + -3 = 0
-3 + -16x + -16x2 = 0 + 16x + -16x
-3 + -16x + -16x2 = 16x + -16x

Combine like terms: 16x + -16x = 0
-3 + -16x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 16x + 16x2) = 0

Factor a trinomial.
-1((3 + 4x)(1 + 4x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 4x)' equal to zero and attempt to solve:

Simplifying
3 + 4x = 0

Solving
3 + 4x = 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 + 4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4x = 0 + -3
4x = 0 + -3

Combine like terms: 0 + -3 = -3
4x = -3

Divide each side by '4'.
x = -0.75

Simplifying
x = -0.75
Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

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

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

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

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {-0.75, -0.25}