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Simplifying 3(-2x + 22)(3x + 4) = 5(-1x + 11)(x + -6) Reorder the terms: 3(22 + -2x)(3x + 4) = 5(-1x + 11)(x + -6) Reorder the terms: 3(22 + -2x)(4 + 3x) = 5(-1x + 11)(x + -6) Multiply (22 + -2x) * (4 + 3x) 3(22(4 + 3x) + -2x * (4 + 3x)) = 5(-1x + 11)(x + -6) 3((4 * 22 + 3x * 22) + -2x * (4 + 3x)) = 5(-1x + 11)(x + -6) 3((88 + 66x) + -2x * (4 + 3x)) = 5(-1x + 11)(x + -6) 3(88 + 66x + (4 * -2x + 3x * -2x)) = 5(-1x + 11)(x + -6) 3(88 + 66x + (-8x + -6x2)) = 5(-1x + 11)(x + -6) Combine like terms: 66x + -8x = 58x 3(88 + 58x + -6x2) = 5(-1x + 11)(x + -6) (88 * 3 + 58x * 3 + -6x2 * 3) = 5(-1x + 11)(x + -6) (264 + 174x + -18x2) = 5(-1x + 11)(x + -6) Reorder the terms: 264 + 174x + -18x2 = 5(11 + -1x)(x + -6) Reorder the terms: 264 + 174x + -18x2 = 5(11 + -1x)(-6 + x) Multiply (11 + -1x) * (-6 + x) 264 + 174x + -18x2 = 5(11(-6 + x) + -1x * (-6 + x)) 264 + 174x + -18x2 = 5((-6 * 11 + x * 11) + -1x * (-6 + x)) 264 + 174x + -18x2 = 5((-66 + 11x) + -1x * (-6 + x)) 264 + 174x + -18x2 = 5(-66 + 11x + (-6 * -1x + x * -1x)) 264 + 174x + -18x2 = 5(-66 + 11x + (6x + -1x2)) Combine like terms: 11x + 6x = 17x 264 + 174x + -18x2 = 5(-66 + 17x + -1x2) 264 + 174x + -18x2 = (-66 * 5 + 17x * 5 + -1x2 * 5) 264 + 174x + -18x2 = (-330 + 85x + -5x2) Solving 264 + 174x + -18x2 = -330 + 85x + -5x2 Solving for variable 'x'. Reorder the terms: 264 + 330 + 174x + -85x + -18x2 + 5x2 = -330 + 85x + -5x2 + 330 + -85x + 5x2 Combine like terms: 264 + 330 = 594 594 + 174x + -85x + -18x2 + 5x2 = -330 + 85x + -5x2 + 330 + -85x + 5x2 Combine like terms: 174x + -85x = 89x 594 + 89x + -18x2 + 5x2 = -330 + 85x + -5x2 + 330 + -85x + 5x2 Combine like terms: -18x2 + 5x2 = -13x2 594 + 89x + -13x2 = -330 + 85x + -5x2 + 330 + -85x + 5x2 Reorder the terms: 594 + 89x + -13x2 = -330 + 330 + 85x + -85x + -5x2 + 5x2 Combine like terms: -330 + 330 = 0 594 + 89x + -13x2 = 0 + 85x + -85x + -5x2 + 5x2 594 + 89x + -13x2 = 85x + -85x + -5x2 + 5x2 Combine like terms: 85x + -85x = 0 594 + 89x + -13x2 = 0 + -5x2 + 5x2 594 + 89x + -13x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 594 + 89x + -13x2 = 0 Factor a trinomial. (11 + -1x)(54 + 13x) = 0Subproblem 1
Set the factor '(11 + -1x)' equal to zero and attempt to solve: Simplifying 11 + -1x = 0 Solving 11 + -1x = 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 + -1x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1x = 0 + -11 -1x = 0 + -11 Combine like terms: 0 + -11 = -11 -1x = -11 Divide each side by '-1'. x = 11 Simplifying x = 11Subproblem 2
Set the factor '(54 + 13x)' equal to zero and attempt to solve: Simplifying 54 + 13x = 0 Solving 54 + 13x = 0 Move all terms containing x to the left, all other terms to the right. Add '-54' to each side of the equation. 54 + -54 + 13x = 0 + -54 Combine like terms: 54 + -54 = 0 0 + 13x = 0 + -54 13x = 0 + -54 Combine like terms: 0 + -54 = -54 13x = -54 Divide each side by '13'. x = -4.153846154 Simplifying x = -4.153846154Solution
x = {11, -4.153846154}
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