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Simplifying (2x + -3)(x + -5x + 1) = 0 Reorder the terms: (-3 + 2x)(x + -5x + 1) = 0 Reorder the terms: (-3 + 2x)(1 + x + -5x) = 0 Combine like terms: x + -5x = -4x (-3 + 2x)(1 + -4x) = 0 Multiply (-3 + 2x) * (1 + -4x) (-3(1 + -4x) + 2x * (1 + -4x)) = 0 ((1 * -3 + -4x * -3) + 2x * (1 + -4x)) = 0 ((-3 + 12x) + 2x * (1 + -4x)) = 0 (-3 + 12x + (1 * 2x + -4x * 2x)) = 0 (-3 + 12x + (2x + -8x2)) = 0 Combine like terms: 12x + 2x = 14x (-3 + 14x + -8x2) = 0 Solving -3 + 14x + -8x2 = 0 Solving for variable 'x'. Factor a trinomial. (-3 + 2x)(1 + -4x) = 0Subproblem 1
Set the factor '(-3 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 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 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Divide each side by '2'. x = 1.5 Simplifying x = 1.5Subproblem 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 = {1.5, 0.25}
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