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Simplifying (1 + -2x)(4x + -3) = 0 Reorder the terms: (1 + -2x)(-3 + 4x) = 0 Multiply (1 + -2x) * (-3 + 4x) (1(-3 + 4x) + -2x * (-3 + 4x)) = 0 ((-3 * 1 + 4x * 1) + -2x * (-3 + 4x)) = 0 ((-3 + 4x) + -2x * (-3 + 4x)) = 0 (-3 + 4x + (-3 * -2x + 4x * -2x)) = 0 (-3 + 4x + (6x + -8x2)) = 0 Combine like terms: 4x + 6x = 10x (-3 + 10x + -8x2) = 0 Solving -3 + 10x + -8x2 = 0 Solving for variable 'x'. Factor a trinomial. (-3 + 4x)(1 + -2x) = 0Subproblem 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 + -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 = {0.75, 0.5}
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