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Simplifying (2x + 5)(3x + -9) = 14x + -56 Reorder the terms: (5 + 2x)(3x + -9) = 14x + -56 Reorder the terms: (5 + 2x)(-9 + 3x) = 14x + -56 Multiply (5 + 2x) * (-9 + 3x) (5(-9 + 3x) + 2x * (-9 + 3x)) = 14x + -56 ((-9 * 5 + 3x * 5) + 2x * (-9 + 3x)) = 14x + -56 ((-45 + 15x) + 2x * (-9 + 3x)) = 14x + -56 (-45 + 15x + (-9 * 2x + 3x * 2x)) = 14x + -56 (-45 + 15x + (-18x + 6x2)) = 14x + -56 Combine like terms: 15x + -18x = -3x (-45 + -3x + 6x2) = 14x + -56 Reorder the terms: -45 + -3x + 6x2 = -56 + 14x Solving -45 + -3x + 6x2 = -56 + 14x Solving for variable 'x'. Reorder the terms: -45 + 56 + -3x + -14x + 6x2 = -56 + 14x + 56 + -14x Combine like terms: -45 + 56 = 11 11 + -3x + -14x + 6x2 = -56 + 14x + 56 + -14x Combine like terms: -3x + -14x = -17x 11 + -17x + 6x2 = -56 + 14x + 56 + -14x Reorder the terms: 11 + -17x + 6x2 = -56 + 56 + 14x + -14x Combine like terms: -56 + 56 = 0 11 + -17x + 6x2 = 0 + 14x + -14x 11 + -17x + 6x2 = 14x + -14x Combine like terms: 14x + -14x = 0 11 + -17x + 6x2 = 0 Factor a trinomial. (1 + -1x)(11 + -6x) = 0Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(11 + -6x)' equal to zero and attempt to solve: Simplifying 11 + -6x = 0 Solving 11 + -6x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -6x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -6x = 0 + -11 -6x = 0 + -11 Combine like terms: 0 + -11 = -11 -6x = -11 Divide each side by '-6'. x = 1.833333333 Simplifying x = 1.833333333Solution
x = {1, 1.833333333}
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