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Simplifying 0 = (4x + -7)(3x + 1) Reorder the terms: 0 = (-7 + 4x)(3x + 1) Reorder the terms: 0 = (-7 + 4x)(1 + 3x) Multiply (-7 + 4x) * (1 + 3x) 0 = (-7(1 + 3x) + 4x * (1 + 3x)) 0 = ((1 * -7 + 3x * -7) + 4x * (1 + 3x)) 0 = ((-7 + -21x) + 4x * (1 + 3x)) 0 = (-7 + -21x + (1 * 4x + 3x * 4x)) 0 = (-7 + -21x + (4x + 12x2)) Combine like terms: -21x + 4x = -17x 0 = (-7 + -17x + 12x2) Solving 0 = -7 + -17x + 12x2 Solving for variable 'x'. Combine like terms: 0 + 7 = 7 7 + 17x + -12x2 = -7 + -17x + 12x2 + 7 + 17x + -12x2 Reorder the terms: 7 + 17x + -12x2 = -7 + 7 + -17x + 17x + 12x2 + -12x2 Combine like terms: -7 + 7 = 0 7 + 17x + -12x2 = 0 + -17x + 17x + 12x2 + -12x2 7 + 17x + -12x2 = -17x + 17x + 12x2 + -12x2 Combine like terms: -17x + 17x = 0 7 + 17x + -12x2 = 0 + 12x2 + -12x2 7 + 17x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 7 + 17x + -12x2 = 0 Factor a trinomial. (7 + -4x)(1 + 3x) = 0Subproblem 1
Set the factor '(7 + -4x)' equal to zero and attempt to solve: Simplifying 7 + -4x = 0 Solving 7 + -4x = 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 + -4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4x = 0 + -7 -4x = 0 + -7 Combine like terms: 0 + -7 = -7 -4x = -7 Divide each side by '-4'. x = 1.75 Simplifying x = 1.75Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {1.75, -0.3333333333}
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