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Simplifying (5x2 + -3x)(8x2 + 4x) = 0 Reorder the terms: (-3x + 5x2)(8x2 + 4x) = 0 Reorder the terms: (-3x + 5x2)(4x + 8x2) = 0 Multiply (-3x + 5x2) * (4x + 8x2) (-3x * (4x + 8x2) + 5x2 * (4x + 8x2)) = 0 ((4x * -3x + 8x2 * -3x) + 5x2 * (4x + 8x2)) = 0 ((-12x2 + -24x3) + 5x2 * (4x + 8x2)) = 0 (-12x2 + -24x3 + (4x * 5x2 + 8x2 * 5x2)) = 0 (-12x2 + -24x3 + (20x3 + 40x4)) = 0 Combine like terms: -24x3 + 20x3 = -4x3 (-12x2 + -4x3 + 40x4) = 0 Solving -12x2 + -4x3 + 40x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x2'. 4x2(-3 + -1x + 10x2) = 0 Factor a trinomial. 4x2((-1 + -2x)(3 + -5x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 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 = -0.5Subproblem 3
Set the factor '(3 + -5x)' equal to zero and attempt to solve: Simplifying 3 + -5x = 0 Solving 3 + -5x = 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 + -5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x = 0 + -3 -5x = 0 + -3 Combine like terms: 0 + -3 = -3 -5x = -3 Divide each side by '-5'. x = 0.6 Simplifying x = 0.6Solution
x = {0, -0.5, 0.6}
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