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Simplifying 0 = 3x2 + 24x + 21 Reorder the terms: 0 = 21 + 24x + 3x2 Solving 0 = 21 + 24x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -21 = -21 -21 + -24x + -3x2 = 21 + 24x + 3x2 + -21 + -24x + -3x2 Reorder the terms: -21 + -24x + -3x2 = 21 + -21 + 24x + -24x + 3x2 + -3x2 Combine like terms: 21 + -21 = 0 -21 + -24x + -3x2 = 0 + 24x + -24x + 3x2 + -3x2 -21 + -24x + -3x2 = 24x + -24x + 3x2 + -3x2 Combine like terms: 24x + -24x = 0 -21 + -24x + -3x2 = 0 + 3x2 + -3x2 -21 + -24x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -21 + -24x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(7 + 8x + x2) = 0 Factor a trinomial. -3((7 + x)(1 + x)) = 0 Ignore the factor -3.Subproblem 1
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 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {-7, -1}
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