0=8x^2+2x-3

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Solution for 0=8x^2+2x-3 equation:


Simplifying
0 = 8x2 + 2x + -3

Reorder the terms:
0 = -3 + 2x + 8x2

Solving
0 = -3 + 2x + 8x2

Solving for variable 'x'.

Combine like terms: 0 + 3 = 3
3 + -2x + -8x2 = -3 + 2x + 8x2 + 3 + -2x + -8x2

Reorder the terms:
3 + -2x + -8x2 = -3 + 3 + 2x + -2x + 8x2 + -8x2

Combine like terms: -3 + 3 = 0
3 + -2x + -8x2 = 0 + 2x + -2x + 8x2 + -8x2
3 + -2x + -8x2 = 2x + -2x + 8x2 + -8x2

Combine like terms: 2x + -2x = 0
3 + -2x + -8x2 = 0 + 8x2 + -8x2
3 + -2x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
3 + -2x + -8x2 = 0

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

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 '(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 = {0.5, -0.75}

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