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Simplifying 4x2 + 10x + -5 = x2 + -3x + -9 Reorder the terms: -5 + 10x + 4x2 = x2 + -3x + -9 Reorder the terms: -5 + 10x + 4x2 = -9 + -3x + x2 Solving -5 + 10x + 4x2 = -9 + -3x + x2 Solving for variable 'x'. Reorder the terms: -5 + 9 + 10x + 3x + 4x2 + -1x2 = -9 + -3x + x2 + 9 + 3x + -1x2 Combine like terms: -5 + 9 = 4 4 + 10x + 3x + 4x2 + -1x2 = -9 + -3x + x2 + 9 + 3x + -1x2 Combine like terms: 10x + 3x = 13x 4 + 13x + 4x2 + -1x2 = -9 + -3x + x2 + 9 + 3x + -1x2 Combine like terms: 4x2 + -1x2 = 3x2 4 + 13x + 3x2 = -9 + -3x + x2 + 9 + 3x + -1x2 Reorder the terms: 4 + 13x + 3x2 = -9 + 9 + -3x + 3x + x2 + -1x2 Combine like terms: -9 + 9 = 0 4 + 13x + 3x2 = 0 + -3x + 3x + x2 + -1x2 4 + 13x + 3x2 = -3x + 3x + x2 + -1x2 Combine like terms: -3x + 3x = 0 4 + 13x + 3x2 = 0 + x2 + -1x2 4 + 13x + 3x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 4 + 13x + 3x2 = 0 Factor a trinomial. (4 + x)(1 + 3x) = 0Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {-4, -0.3333333333}
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