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Simplifying 4x2 + -13x + 21 = 3x + 6 Reorder the terms: 21 + -13x + 4x2 = 3x + 6 Reorder the terms: 21 + -13x + 4x2 = 6 + 3x Solving 21 + -13x + 4x2 = 6 + 3x Solving for variable 'x'. Reorder the terms: 21 + -6 + -13x + -3x + 4x2 = 6 + 3x + -6 + -3x Combine like terms: 21 + -6 = 15 15 + -13x + -3x + 4x2 = 6 + 3x + -6 + -3x Combine like terms: -13x + -3x = -16x 15 + -16x + 4x2 = 6 + 3x + -6 + -3x Reorder the terms: 15 + -16x + 4x2 = 6 + -6 + 3x + -3x Combine like terms: 6 + -6 = 0 15 + -16x + 4x2 = 0 + 3x + -3x 15 + -16x + 4x2 = 3x + -3x Combine like terms: 3x + -3x = 0 15 + -16x + 4x2 = 0 Factor a trinomial. (3 + -2x)(5 + -2x) = 0Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {1.5, 2.5}
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