4x=16x^2-6

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Solution for 4x=16x^2-6 equation:


Simplifying
4x = 16x2 + -6

Reorder the terms:
4x = -6 + 16x2

Solving
4x = -6 + 16x2

Solving for variable 'x'.

Reorder the terms:
6 + 4x + -16x2 = -6 + 16x2 + 6 + -16x2

Reorder the terms:
6 + 4x + -16x2 = -6 + 6 + 16x2 + -16x2

Combine like terms: -6 + 6 = 0
6 + 4x + -16x2 = 0 + 16x2 + -16x2
6 + 4x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
6 + 4x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 2x + -8x2) = 0

Factor a trinomial.
2((3 + -4x)(1 + 2x)) = 0

Ignore the factor 2.

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 + 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

Solution

x = {0.75, -0.5}

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