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Simplifying (4x + 3)(5x + -3) = -1(173x + -124) Reorder the terms: (3 + 4x)(5x + -3) = -1(173x + -124) Reorder the terms: (3 + 4x)(-3 + 5x) = -1(173x + -124) Multiply (3 + 4x) * (-3 + 5x) (3(-3 + 5x) + 4x * (-3 + 5x)) = -1(173x + -124) ((-3 * 3 + 5x * 3) + 4x * (-3 + 5x)) = -1(173x + -124) ((-9 + 15x) + 4x * (-3 + 5x)) = -1(173x + -124) (-9 + 15x + (-3 * 4x + 5x * 4x)) = -1(173x + -124) (-9 + 15x + (-12x + 20x2)) = -1(173x + -124) Combine like terms: 15x + -12x = 3x (-9 + 3x + 20x2) = -1(173x + -124) Reorder the terms: -9 + 3x + 20x2 = -1(-124 + 173x) -9 + 3x + 20x2 = (-124 * -1 + 173x * -1) -9 + 3x + 20x2 = (124 + -173x) Solving -9 + 3x + 20x2 = 124 + -173x Solving for variable 'x'. Reorder the terms: -9 + -124 + 3x + 173x + 20x2 = 124 + -173x + -124 + 173x Combine like terms: -9 + -124 = -133 -133 + 3x + 173x + 20x2 = 124 + -173x + -124 + 173x Combine like terms: 3x + 173x = 176x -133 + 176x + 20x2 = 124 + -173x + -124 + 173x Reorder the terms: -133 + 176x + 20x2 = 124 + -124 + -173x + 173x Combine like terms: 124 + -124 = 0 -133 + 176x + 20x2 = 0 + -173x + 173x -133 + 176x + 20x2 = -173x + 173x Combine like terms: -173x + 173x = 0 -133 + 176x + 20x2 = 0 Factor a trinomial. (-19 + -2x)(7 + -10x) = 0Subproblem 1
Set the factor '(-19 + -2x)' equal to zero and attempt to solve: Simplifying -19 + -2x = 0 Solving -19 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + -2x = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -2x = 0 + 19 -2x = 0 + 19 Combine like terms: 0 + 19 = 19 -2x = 19 Divide each side by '-2'. x = -9.5 Simplifying x = -9.5Subproblem 2
Set the factor '(7 + -10x)' equal to zero and attempt to solve: Simplifying 7 + -10x = 0 Solving 7 + -10x = 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 + -10x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -10x = 0 + -7 -10x = 0 + -7 Combine like terms: 0 + -7 = -7 -10x = -7 Divide each side by '-10'. x = 0.7 Simplifying x = 0.7Solution
x = {-9.5, 0.7}
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