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Simplifying 4x(x + -5) = (2x + 1)(x + -5) Reorder the terms: 4x(-5 + x) = (2x + 1)(x + -5) (-5 * 4x + x * 4x) = (2x + 1)(x + -5) (-20x + 4x2) = (2x + 1)(x + -5) Reorder the terms: -20x + 4x2 = (1 + 2x)(x + -5) Reorder the terms: -20x + 4x2 = (1 + 2x)(-5 + x) Multiply (1 + 2x) * (-5 + x) -20x + 4x2 = (1(-5 + x) + 2x * (-5 + x)) -20x + 4x2 = ((-5 * 1 + x * 1) + 2x * (-5 + x)) -20x + 4x2 = ((-5 + 1x) + 2x * (-5 + x)) -20x + 4x2 = (-5 + 1x + (-5 * 2x + x * 2x)) -20x + 4x2 = (-5 + 1x + (-10x + 2x2)) Combine like terms: 1x + -10x = -9x -20x + 4x2 = (-5 + -9x + 2x2) Solving -20x + 4x2 = -5 + -9x + 2x2 Solving for variable 'x'. Reorder the terms: 5 + -20x + 9x + 4x2 + -2x2 = -5 + -9x + 2x2 + 5 + 9x + -2x2 Combine like terms: -20x + 9x = -11x 5 + -11x + 4x2 + -2x2 = -5 + -9x + 2x2 + 5 + 9x + -2x2 Combine like terms: 4x2 + -2x2 = 2x2 5 + -11x + 2x2 = -5 + -9x + 2x2 + 5 + 9x + -2x2 Reorder the terms: 5 + -11x + 2x2 = -5 + 5 + -9x + 9x + 2x2 + -2x2 Combine like terms: -5 + 5 = 0 5 + -11x + 2x2 = 0 + -9x + 9x + 2x2 + -2x2 5 + -11x + 2x2 = -9x + 9x + 2x2 + -2x2 Combine like terms: -9x + 9x = 0 5 + -11x + 2x2 = 0 + 2x2 + -2x2 5 + -11x + 2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 5 + -11x + 2x2 = 0 Factor a trinomial. (1 + -2x)(5 + -1x) = 0Subproblem 1
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 = 0.5Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {0.5, 5}
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