(2x-6)(8x-3)=0

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Solution for (2x-6)(8x-3)=0 equation:


Simplifying
(2x + -6)(8x + -3) = 0

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

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

Multiply (-6 + 2x) * (-3 + 8x)
(-6(-3 + 8x) + 2x * (-3 + 8x)) = 0
((-3 * -6 + 8x * -6) + 2x * (-3 + 8x)) = 0
((18 + -48x) + 2x * (-3 + 8x)) = 0
(18 + -48x + (-3 * 2x + 8x * 2x)) = 0
(18 + -48x + (-6x + 16x2)) = 0

Combine like terms: -48x + -6x = -54x
(18 + -54x + 16x2) = 0

Solving
18 + -54x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -27x + 8x2) = 0

Factor a trinomial.
2((3 + -8x)(3 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(3 + -8x)' equal to zero and attempt to solve: Simplifying 3 + -8x = 0 Solving 3 + -8x = 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 + -8x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8x = 0 + -3 -8x = 0 + -3 Combine like terms: 0 + -3 = -3 -8x = -3 Divide each side by '-8'. x = 0.375 Simplifying x = 0.375

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {0.375, 3}

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