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Simplifying (2x + -3)(9x + -7) = -8(x + -2) Reorder the terms: (-3 + 2x)(9x + -7) = -8(x + -2) Reorder the terms: (-3 + 2x)(-7 + 9x) = -8(x + -2) Multiply (-3 + 2x) * (-7 + 9x) (-3(-7 + 9x) + 2x * (-7 + 9x)) = -8(x + -2) ((-7 * -3 + 9x * -3) + 2x * (-7 + 9x)) = -8(x + -2) ((21 + -27x) + 2x * (-7 + 9x)) = -8(x + -2) (21 + -27x + (-7 * 2x + 9x * 2x)) = -8(x + -2) (21 + -27x + (-14x + 18x2)) = -8(x + -2) Combine like terms: -27x + -14x = -41x (21 + -41x + 18x2) = -8(x + -2) Reorder the terms: 21 + -41x + 18x2 = -8(-2 + x) 21 + -41x + 18x2 = (-2 * -8 + x * -8) 21 + -41x + 18x2 = (16 + -8x) Solving 21 + -41x + 18x2 = 16 + -8x Solving for variable 'x'. Reorder the terms: 21 + -16 + -41x + 8x + 18x2 = 16 + -8x + -16 + 8x Combine like terms: 21 + -16 = 5 5 + -41x + 8x + 18x2 = 16 + -8x + -16 + 8x Combine like terms: -41x + 8x = -33x 5 + -33x + 18x2 = 16 + -8x + -16 + 8x Reorder the terms: 5 + -33x + 18x2 = 16 + -16 + -8x + 8x Combine like terms: 16 + -16 = 0 5 + -33x + 18x2 = 0 + -8x + 8x 5 + -33x + 18x2 = -8x + 8x Combine like terms: -8x + 8x = 0 5 + -33x + 18x2 = 0 Factor a trinomial. (1 + -6x)(5 + -3x) = 0Subproblem 1
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 = 0.1666666667Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 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 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Divide each side by '-3'. x = 1.666666667 Simplifying x = 1.666666667Solution
x = {0.1666666667, 1.666666667}
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