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Simplifying 4x(x2 + -3x) = 2x(4x + -8) + -9x Reorder the terms: 4x(-3x + x2) = 2x(4x + -8) + -9x (-3x * 4x + x2 * 4x) = 2x(4x + -8) + -9x (-12x2 + 4x3) = 2x(4x + -8) + -9x Reorder the terms: -12x2 + 4x3 = 2x(-8 + 4x) + -9x -12x2 + 4x3 = (-8 * 2x + 4x * 2x) + -9x -12x2 + 4x3 = (-16x + 8x2) + -9x Reorder the terms: -12x2 + 4x3 = -16x + -9x + 8x2 Combine like terms: -16x + -9x = -25x -12x2 + 4x3 = -25x + 8x2 Solving -12x2 + 4x3 = -25x + 8x2 Solving for variable 'x'. Reorder the terms: 25x + -12x2 + -8x2 + 4x3 = -25x + 8x2 + 25x + -8x2 Combine like terms: -12x2 + -8x2 = -20x2 25x + -20x2 + 4x3 = -25x + 8x2 + 25x + -8x2 Reorder the terms: 25x + -20x2 + 4x3 = -25x + 25x + 8x2 + -8x2 Combine like terms: -25x + 25x = 0 25x + -20x2 + 4x3 = 0 + 8x2 + -8x2 25x + -20x2 + 4x3 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 25x + -20x2 + 4x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(25 + -20x + 4x2) = 0 Factor a trinomial. x((5 + -2x)(5 + -2x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Subproblem 3
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {0, 2.5, 2.5}
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