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Simplifying (x + -7)(3x + -5) + -1(9x + -4)(x + -7) = 0 Reorder the terms: (-7 + x)(3x + -5) + -1(9x + -4)(x + -7) = 0 Reorder the terms: (-7 + x)(-5 + 3x) + -1(9x + -4)(x + -7) = 0 Multiply (-7 + x) * (-5 + 3x) (-7(-5 + 3x) + x(-5 + 3x)) + -1(9x + -4)(x + -7) = 0 ((-5 * -7 + 3x * -7) + x(-5 + 3x)) + -1(9x + -4)(x + -7) = 0 ((35 + -21x) + x(-5 + 3x)) + -1(9x + -4)(x + -7) = 0 (35 + -21x + (-5 * x + 3x * x)) + -1(9x + -4)(x + -7) = 0 (35 + -21x + (-5x + 3x2)) + -1(9x + -4)(x + -7) = 0 Combine like terms: -21x + -5x = -26x (35 + -26x + 3x2) + -1(9x + -4)(x + -7) = 0 Reorder the terms: 35 + -26x + 3x2 + -1(-4 + 9x)(x + -7) = 0 Reorder the terms: 35 + -26x + 3x2 + -1(-4 + 9x)(-7 + x) = 0 Multiply (-4 + 9x) * (-7 + x) 35 + -26x + 3x2 + -1(-4(-7 + x) + 9x * (-7 + x)) = 0 35 + -26x + 3x2 + -1((-7 * -4 + x * -4) + 9x * (-7 + x)) = 0 35 + -26x + 3x2 + -1((28 + -4x) + 9x * (-7 + x)) = 0 35 + -26x + 3x2 + -1(28 + -4x + (-7 * 9x + x * 9x)) = 0 35 + -26x + 3x2 + -1(28 + -4x + (-63x + 9x2)) = 0 Combine like terms: -4x + -63x = -67x 35 + -26x + 3x2 + -1(28 + -67x + 9x2) = 0 35 + -26x + 3x2 + (28 * -1 + -67x * -1 + 9x2 * -1) = 0 35 + -26x + 3x2 + (-28 + 67x + -9x2) = 0 Reorder the terms: 35 + -28 + -26x + 67x + 3x2 + -9x2 = 0 Combine like terms: 35 + -28 = 7 7 + -26x + 67x + 3x2 + -9x2 = 0 Combine like terms: -26x + 67x = 41x 7 + 41x + 3x2 + -9x2 = 0 Combine like terms: 3x2 + -9x2 = -6x2 7 + 41x + -6x2 = 0 Solving 7 + 41x + -6x2 = 0 Solving for variable 'x'. Factor a trinomial. (7 + -1x)(1 + 6x) = 0Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Subproblem 2
Set the factor '(1 + 6x)' equal to zero and attempt to solve: Simplifying 1 + 6x = 0 Solving 1 + 6x = 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 + 6x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6x = 0 + -1 6x = 0 + -1 Combine like terms: 0 + -1 = -1 6x = -1 Divide each side by '6'. x = -0.1666666667 Simplifying x = -0.1666666667Solution
x = {7, -0.1666666667}
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