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Simplifying 3x(4x + 7) + -7(4x + 7) = 0 Reorder the terms: 3x(7 + 4x) + -7(4x + 7) = 0 (7 * 3x + 4x * 3x) + -7(4x + 7) = 0 (21x + 12x2) + -7(4x + 7) = 0 Reorder the terms: 21x + 12x2 + -7(7 + 4x) = 0 21x + 12x2 + (7 * -7 + 4x * -7) = 0 21x + 12x2 + (-49 + -28x) = 0 Reorder the terms: -49 + 21x + -28x + 12x2 = 0 Combine like terms: 21x + -28x = -7x -49 + -7x + 12x2 = 0 Solving -49 + -7x + 12x2 = 0 Solving for variable 'x'. Factor a trinomial. (-7 + -4x)(7 + -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 '(7 + -3x)' equal to zero and attempt to solve: Simplifying 7 + -3x = 0 Solving 7 + -3x = 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 + -3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3x = 0 + -7 -3x = 0 + -7 Combine like terms: 0 + -7 = -7 -3x = -7 Divide each side by '-3'. x = 2.333333333 Simplifying x = 2.333333333Solution
x = {-1.75, 2.333333333}
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