4*x-3-16*x^2=9-24*x

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Solution for 4*x-3-16*x^2=9-24*x equation: 


Simplifying
4x + -3 + -16x2 = 9 + -24x

Reorder the terms:
-3 + 4x + -16x2 = 9 + -24x

Solving
-3 + 4x + -16x2 = 9 + -24x

Solving for variable 'x'.

Reorder the terms:
-3 + -9 + 4x + 24x + -16x2 = 9 + -24x + -9 + 24x

Combine like terms: -3 + -9 = -12
-12 + 4x + 24x + -16x2 = 9 + -24x + -9 + 24x

Combine like terms: 4x + 24x = 28x
-12 + 28x + -16x2 = 9 + -24x + -9 + 24x

Reorder the terms:
-12 + 28x + -16x2 = 9 + -9 + -24x + 24x

Combine like terms: 9 + -9 = 0
-12 + 28x + -16x2 = 0 + -24x + 24x
-12 + 28x + -16x2 = -24x + 24x

Combine like terms: -24x + 24x = 0
-12 + 28x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + 7x + -4x2) = 0

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

Ignore the factor 4.

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

Simplifying
-1 + x = 0

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

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

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

Simplifying
x = 1

Subproblem 2
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
Solution
x = {1, 0.75}

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