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Simplifying (8x + 2)(6x + -3) = 0 Reorder the terms: (2 + 8x)(6x + -3) = 0 Reorder the terms: (2 + 8x)(-3 + 6x) = 0 Multiply (2 + 8x) * (-3 + 6x) (2(-3 + 6x) + 8x * (-3 + 6x)) = 0 ((-3 * 2 + 6x * 2) + 8x * (-3 + 6x)) = 0 ((-6 + 12x) + 8x * (-3 + 6x)) = 0 (-6 + 12x + (-3 * 8x + 6x * 8x)) = 0 (-6 + 12x + (-24x + 48x2)) = 0 Combine like terms: 12x + -24x = -12x (-6 + -12x + 48x2) = 0 Solving -6 + -12x + 48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-1 + -2x + 8x2) = 0 Factor a trinomial. 6((-1 + -4x)(1 + -2x)) = 0 Ignore the factor 6.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 = -0.25Subproblem 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 = 0.5Solution
x = {-0.25, 0.5}
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