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Simplifying x(9x + 3) = 4x2 + -5x + 21 Reorder the terms: x(3 + 9x) = 4x2 + -5x + 21 (3 * x + 9x * x) = 4x2 + -5x + 21 (3x + 9x2) = 4x2 + -5x + 21 Reorder the terms: 3x + 9x2 = 21 + -5x + 4x2 Solving 3x + 9x2 = 21 + -5x + 4x2 Solving for variable 'x'. Reorder the terms: -21 + 3x + 5x + 9x2 + -4x2 = 21 + -5x + 4x2 + -21 + 5x + -4x2 Combine like terms: 3x + 5x = 8x -21 + 8x + 9x2 + -4x2 = 21 + -5x + 4x2 + -21 + 5x + -4x2 Combine like terms: 9x2 + -4x2 = 5x2 -21 + 8x + 5x2 = 21 + -5x + 4x2 + -21 + 5x + -4x2 Reorder the terms: -21 + 8x + 5x2 = 21 + -21 + -5x + 5x + 4x2 + -4x2 Combine like terms: 21 + -21 = 0 -21 + 8x + 5x2 = 0 + -5x + 5x + 4x2 + -4x2 -21 + 8x + 5x2 = -5x + 5x + 4x2 + -4x2 Combine like terms: -5x + 5x = 0 -21 + 8x + 5x2 = 0 + 4x2 + -4x2 -21 + 8x + 5x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -21 + 8x + 5x2 = 0 Factor a trinomial. (-3 + -1x)(7 + -5x) = 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 '(7 + -5x)' equal to zero and attempt to solve: Simplifying 7 + -5x = 0 Solving 7 + -5x = 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 + -5x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5x = 0 + -7 -5x = 0 + -7 Combine like terms: 0 + -7 = -7 -5x = -7 Divide each side by '-5'. x = 1.4 Simplifying x = 1.4Solution
x = {-3, 1.4}
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