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Simplifying 0 = 7x3 + -16x2 + -15x Reorder the terms: 0 = -15x + -16x2 + 7x3 Solving 0 = -15x + -16x2 + 7x3 Solving for variable 'x'. Remove the zero: 15x + 16x2 + -7x3 = -15x + -16x2 + 7x3 + 15x + 16x2 + -7x3 Reorder the terms: 15x + 16x2 + -7x3 = -15x + 15x + -16x2 + 16x2 + 7x3 + -7x3 Combine like terms: -15x + 15x = 0 15x + 16x2 + -7x3 = 0 + -16x2 + 16x2 + 7x3 + -7x3 15x + 16x2 + -7x3 = -16x2 + 16x2 + 7x3 + -7x3 Combine like terms: -16x2 + 16x2 = 0 15x + 16x2 + -7x3 = 0 + 7x3 + -7x3 15x + 16x2 + -7x3 = 7x3 + -7x3 Combine like terms: 7x3 + -7x3 = 0 15x + 16x2 + -7x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(15 + 16x + -7x2) = 0 Factor a trinomial. x((3 + -1x)(5 + 7x)) = 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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 3
Set the factor '(5 + 7x)' equal to zero and attempt to solve: Simplifying 5 + 7x = 0 Solving 5 + 7x = 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 + 7x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 7x = 0 + -5 7x = 0 + -5 Combine like terms: 0 + -5 = -5 7x = -5 Divide each side by '7'. x = -0.7142857143 Simplifying x = -0.7142857143Solution
x = {0, 3, -0.7142857143}
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