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Simplifying 4x3 + 28x2 = -12x2 + -84x Reorder the terms: 28x2 + 4x3 = -12x2 + -84x Reorder the terms: 28x2 + 4x3 = -84x + -12x2 Solving 28x2 + 4x3 = -84x + -12x2 Solving for variable 'x'. Reorder the terms: 84x + 28x2 + 12x2 + 4x3 = -84x + -12x2 + 84x + 12x2 Combine like terms: 28x2 + 12x2 = 40x2 84x + 40x2 + 4x3 = -84x + -12x2 + 84x + 12x2 Reorder the terms: 84x + 40x2 + 4x3 = -84x + 84x + -12x2 + 12x2 Combine like terms: -84x + 84x = 0 84x + 40x2 + 4x3 = 0 + -12x2 + 12x2 84x + 40x2 + 4x3 = -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 84x + 40x2 + 4x3 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(21 + 10x + x2) = 0 Factor a trinomial. 4x((7 + x)(3 + x)) = 0 Ignore the factor 4.Subproblem 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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Subproblem 3
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {0, -7, -3}
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