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Simplifying 5x + 3 = x2 + 4x + -3 Reorder the terms: 3 + 5x = x2 + 4x + -3 Reorder the terms: 3 + 5x = -3 + 4x + x2 Solving 3 + 5x = -3 + 4x + x2 Solving for variable 'x'. Reorder the terms: 3 + 3 + 5x + -4x + -1x2 = -3 + 4x + x2 + 3 + -4x + -1x2 Combine like terms: 3 + 3 = 6 6 + 5x + -4x + -1x2 = -3 + 4x + x2 + 3 + -4x + -1x2 Combine like terms: 5x + -4x = 1x 6 + 1x + -1x2 = -3 + 4x + x2 + 3 + -4x + -1x2 Reorder the terms: 6 + 1x + -1x2 = -3 + 3 + 4x + -4x + x2 + -1x2 Combine like terms: -3 + 3 = 0 6 + 1x + -1x2 = 0 + 4x + -4x + x2 + -1x2 6 + 1x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 6 + 1x + -1x2 = 0 + x2 + -1x2 6 + 1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 6 + 1x + -1x2 = 0 Factor a trinomial. (3 + -1x)(2 + x) = 0Subproblem 1
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 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {3, -2}
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