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Simplifying 3(-1x + 11)(3x + 4) = 5(-1x + 11)(x + -6) Reorder the terms: 3(11 + -1x)(3x + 4) = 5(-1x + 11)(x + -6) Reorder the terms: 3(11 + -1x)(4 + 3x) = 5(-1x + 11)(x + -6) Multiply (11 + -1x) * (4 + 3x) 3(11(4 + 3x) + -1x * (4 + 3x)) = 5(-1x + 11)(x + -6) 3((4 * 11 + 3x * 11) + -1x * (4 + 3x)) = 5(-1x + 11)(x + -6) 3((44 + 33x) + -1x * (4 + 3x)) = 5(-1x + 11)(x + -6) 3(44 + 33x + (4 * -1x + 3x * -1x)) = 5(-1x + 11)(x + -6) 3(44 + 33x + (-4x + -3x2)) = 5(-1x + 11)(x + -6) Combine like terms: 33x + -4x = 29x 3(44 + 29x + -3x2) = 5(-1x + 11)(x + -6) (44 * 3 + 29x * 3 + -3x2 * 3) = 5(-1x + 11)(x + -6) (132 + 87x + -9x2) = 5(-1x + 11)(x + -6) Reorder the terms: 132 + 87x + -9x2 = 5(11 + -1x)(x + -6) Reorder the terms: 132 + 87x + -9x2 = 5(11 + -1x)(-6 + x) Multiply (11 + -1x) * (-6 + x) 132 + 87x + -9x2 = 5(11(-6 + x) + -1x * (-6 + x)) 132 + 87x + -9x2 = 5((-6 * 11 + x * 11) + -1x * (-6 + x)) 132 + 87x + -9x2 = 5((-66 + 11x) + -1x * (-6 + x)) 132 + 87x + -9x2 = 5(-66 + 11x + (-6 * -1x + x * -1x)) 132 + 87x + -9x2 = 5(-66 + 11x + (6x + -1x2)) Combine like terms: 11x + 6x = 17x 132 + 87x + -9x2 = 5(-66 + 17x + -1x2) 132 + 87x + -9x2 = (-66 * 5 + 17x * 5 + -1x2 * 5) 132 + 87x + -9x2 = (-330 + 85x + -5x2) Solving 132 + 87x + -9x2 = -330 + 85x + -5x2 Solving for variable 'x'. Reorder the terms: 132 + 330 + 87x + -85x + -9x2 + 5x2 = -330 + 85x + -5x2 + 330 + -85x + 5x2 Combine like terms: 132 + 330 = 462 462 + 87x + -85x + -9x2 + 5x2 = -330 + 85x + -5x2 + 330 + -85x + 5x2 Combine like terms: 87x + -85x = 2x 462 + 2x + -9x2 + 5x2 = -330 + 85x + -5x2 + 330 + -85x + 5x2 Combine like terms: -9x2 + 5x2 = -4x2 462 + 2x + -4x2 = -330 + 85x + -5x2 + 330 + -85x + 5x2 Reorder the terms: 462 + 2x + -4x2 = -330 + 330 + 85x + -85x + -5x2 + 5x2 Combine like terms: -330 + 330 = 0 462 + 2x + -4x2 = 0 + 85x + -85x + -5x2 + 5x2 462 + 2x + -4x2 = 85x + -85x + -5x2 + 5x2 Combine like terms: 85x + -85x = 0 462 + 2x + -4x2 = 0 + -5x2 + 5x2 462 + 2x + -4x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 462 + 2x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(231 + x + -2x2) = 0 Factor a trinomial. 2((11 + -1x)(21 + 2x)) = 0 Ignore the factor 2.Subproblem 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 '(21 + 2x)' equal to zero and attempt to solve: Simplifying 21 + 2x = 0 Solving 21 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + 2x = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 2x = 0 + -21 2x = 0 + -21 Combine like terms: 0 + -21 = -21 2x = -21 Divide each side by '2'. x = -10.5 Simplifying x = -10.5Solution
x = {11, -10.5}
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