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Simplifying (5x3 + 45x2)(28x + -12) = 0 Reorder the terms: (45x2 + 5x3)(28x + -12) = 0 Reorder the terms: (45x2 + 5x3)(-12 + 28x) = 0 Multiply (45x2 + 5x3) * (-12 + 28x) (45x2 * (-12 + 28x) + 5x3 * (-12 + 28x)) = 0 ((-12 * 45x2 + 28x * 45x2) + 5x3 * (-12 + 28x)) = 0 ((-540x2 + 1260x3) + 5x3 * (-12 + 28x)) = 0 (-540x2 + 1260x3 + (-12 * 5x3 + 28x * 5x3)) = 0 (-540x2 + 1260x3 + (-60x3 + 140x4)) = 0 Combine like terms: 1260x3 + -60x3 = 1200x3 (-540x2 + 1200x3 + 140x4) = 0 Solving -540x2 + 1200x3 + 140x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '20x2'. 20x2(-27 + 60x + 7x2) = 0 Factor a trinomial. 20x2((-9 + -1x)(3 + -7x)) = 0 Ignore the factor 20.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 '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9Subproblem 3
Set the factor '(3 + -7x)' equal to zero and attempt to solve: Simplifying 3 + -7x = 0 Solving 3 + -7x = 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 + -7x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7x = 0 + -3 -7x = 0 + -3 Combine like terms: 0 + -3 = -3 -7x = -3 Divide each side by '-7'. x = 0.4285714286 Simplifying x = 0.4285714286Solution
x = {0, -9, 0.4285714286}
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