2(4x+1)(x-1)+3=0

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Solution for 2(4x+1)(x-1)+3=0 equation:


Simplifying
2(4x + 1)(x + -1) + 3 = 0

Reorder the terms:
2(1 + 4x)(x + -1) + 3 = 0

Reorder the terms:
2(1 + 4x)(-1 + x) + 3 = 0

Multiply (1 + 4x) * (-1 + x)
2(1(-1 + x) + 4x * (-1 + x)) + 3 = 0
2((-1 * 1 + x * 1) + 4x * (-1 + x)) + 3 = 0
2((-1 + 1x) + 4x * (-1 + x)) + 3 = 0
2(-1 + 1x + (-1 * 4x + x * 4x)) + 3 = 0
2(-1 + 1x + (-4x + 4x2)) + 3 = 0

Combine like terms: 1x + -4x = -3x
2(-1 + -3x + 4x2) + 3 = 0
(-1 * 2 + -3x * 2 + 4x2 * 2) + 3 = 0
(-2 + -6x + 8x2) + 3 = 0

Reorder the terms:
-2 + 3 + -6x + 8x2 = 0

Combine like terms: -2 + 3 = 1
1 + -6x + 8x2 = 0

Solving
1 + -6x + 8x2 = 0

Solving for variable 'x'.

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

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 + -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 = {0.25, 0.5}

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