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Simplifying 0 = (4x + -3)(2x + -1) Reorder the terms: 0 = (-3 + 4x)(2x + -1) Reorder the terms: 0 = (-3 + 4x)(-1 + 2x) Multiply (-3 + 4x) * (-1 + 2x) 0 = (-3(-1 + 2x) + 4x * (-1 + 2x)) 0 = ((-1 * -3 + 2x * -3) + 4x * (-1 + 2x)) 0 = ((3 + -6x) + 4x * (-1 + 2x)) 0 = (3 + -6x + (-1 * 4x + 2x * 4x)) 0 = (3 + -6x + (-4x + 8x2)) Combine like terms: -6x + -4x = -10x 0 = (3 + -10x + 8x2) Solving 0 = 3 + -10x + 8x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + 10x + -8x2 = 3 + -10x + 8x2 + -3 + 10x + -8x2 Reorder the terms: -3 + 10x + -8x2 = 3 + -3 + -10x + 10x + 8x2 + -8x2 Combine like terms: 3 + -3 = 0 -3 + 10x + -8x2 = 0 + -10x + 10x + 8x2 + -8x2 -3 + 10x + -8x2 = -10x + 10x + 8x2 + -8x2 Combine like terms: -10x + 10x = 0 -3 + 10x + -8x2 = 0 + 8x2 + -8x2 -3 + 10x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -3 + 10x + -8x2 = 0 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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