15=-16x^2+20x+11

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Solution for 15=-16x^2+20x+11 equation: 


Simplifying
15 = -16x2 + 20x + 11

Reorder the terms:
15 = 11 + 20x + -16x2

Solving
15 = 11 + 20x + -16x2

Solving for variable 'x'.

Combine like terms: 15 + -11 = 4
4 + -20x + 16x2 = 11 + 20x + -16x2 + -11 + -20x + 16x2

Reorder the terms:
4 + -20x + 16x2 = 11 + -11 + 20x + -20x + -16x2 + 16x2

Combine like terms: 11 + -11 = 0
4 + -20x + 16x2 = 0 + 20x + -20x + -16x2 + 16x2
4 + -20x + 16x2 = 20x + -20x + -16x2 + 16x2

Combine like terms: 20x + -20x = 0
4 + -20x + 16x2 = 0 + -16x2 + 16x2
4 + -20x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
4 + -20x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + -5x + 4x2) = 0

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

Ignore the factor 4.

Subproblem 1
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

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 = {0.25, 1}

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