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Simplifying (5x2 + 45x)(35x3 + -15x2) = 0 Reorder the terms: (45x + 5x2)(35x3 + -15x2) = 0 Reorder the terms: (45x + 5x2)(-15x2 + 35x3) = 0 Multiply (45x + 5x2) * (-15x2 + 35x3) (45x * (-15x2 + 35x3) + 5x2 * (-15x2 + 35x3)) = 0 ((-15x2 * 45x + 35x3 * 45x) + 5x2 * (-15x2 + 35x3)) = 0 ((-675x3 + 1575x4) + 5x2 * (-15x2 + 35x3)) = 0 (-675x3 + 1575x4 + (-15x2 * 5x2 + 35x3 * 5x2)) = 0 (-675x3 + 1575x4 + (-75x4 + 175x5)) = 0 Combine like terms: 1575x4 + -75x4 = 1500x4 (-675x3 + 1500x4 + 175x5) = 0 Solving -675x3 + 1500x4 + 175x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '25x3'. 25x3(-27 + 60x + 7x2) = 0 Factor a trinomial. 25x3((-9 + -1x)(3 + -7x)) = 0 Ignore the factor 25.Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.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 = {-9, 0.4285714286}
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