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Simplifying 9x(x + -3) = (2x + 5)(x + -3) Reorder the terms: 9x(-3 + x) = (2x + 5)(x + -3) (-3 * 9x + x * 9x) = (2x + 5)(x + -3) (-27x + 9x2) = (2x + 5)(x + -3) Reorder the terms: -27x + 9x2 = (5 + 2x)(x + -3) Reorder the terms: -27x + 9x2 = (5 + 2x)(-3 + x) Multiply (5 + 2x) * (-3 + x) -27x + 9x2 = (5(-3 + x) + 2x * (-3 + x)) -27x + 9x2 = ((-3 * 5 + x * 5) + 2x * (-3 + x)) -27x + 9x2 = ((-15 + 5x) + 2x * (-3 + x)) -27x + 9x2 = (-15 + 5x + (-3 * 2x + x * 2x)) -27x + 9x2 = (-15 + 5x + (-6x + 2x2)) Combine like terms: 5x + -6x = -1x -27x + 9x2 = (-15 + -1x + 2x2) Solving -27x + 9x2 = -15 + -1x + 2x2 Solving for variable 'x'. Reorder the terms: 15 + -27x + x + 9x2 + -2x2 = -15 + -1x + 2x2 + 15 + x + -2x2 Combine like terms: -27x + x = -26x 15 + -26x + 9x2 + -2x2 = -15 + -1x + 2x2 + 15 + x + -2x2 Combine like terms: 9x2 + -2x2 = 7x2 15 + -26x + 7x2 = -15 + -1x + 2x2 + 15 + x + -2x2 Reorder the terms: 15 + -26x + 7x2 = -15 + 15 + -1x + x + 2x2 + -2x2 Combine like terms: -15 + 15 = 0 15 + -26x + 7x2 = 0 + -1x + x + 2x2 + -2x2 15 + -26x + 7x2 = -1x + x + 2x2 + -2x2 Combine like terms: -1x + x = 0 15 + -26x + 7x2 = 0 + 2x2 + -2x2 15 + -26x + 7x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 15 + -26x + 7x2 = 0 Factor a trinomial. (5 + -7x)(3 + -1x) = 0Subproblem 1
Set the factor '(5 + -7x)' equal to zero and attempt to solve: Simplifying 5 + -7x = 0 Solving 5 + -7x = 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 + -7x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7x = 0 + -5 -7x = 0 + -5 Combine like terms: 0 + -5 = -5 -7x = -5 Divide each side by '-7'. x = 0.7142857143 Simplifying x = 0.7142857143Subproblem 2
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 = 3Solution
x = {0.7142857143, 3}
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