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Simplifying (4x + 3)(8x + -2) = 0 Reorder the terms: (3 + 4x)(8x + -2) = 0 Reorder the terms: (3 + 4x)(-2 + 8x) = 0 Multiply (3 + 4x) * (-2 + 8x) (3(-2 + 8x) + 4x * (-2 + 8x)) = 0 ((-2 * 3 + 8x * 3) + 4x * (-2 + 8x)) = 0 ((-6 + 24x) + 4x * (-2 + 8x)) = 0 (-6 + 24x + (-2 * 4x + 8x * 4x)) = 0 (-6 + 24x + (-8x + 32x2)) = 0 Combine like terms: 24x + -8x = 16x (-6 + 16x + 32x2) = 0 Solving -6 + 16x + 32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 8x + 16x2) = 0 Factor a trinomial. 2((-3 + -4x)(1 + -4x)) = 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 = -0.75Subproblem 2
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 = 0.25Solution
x = {-0.75, 0.25}
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