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Simplifying (7x + -49)(12 + -2x) = 0 Reorder the terms: (-49 + 7x)(12 + -2x) = 0 Multiply (-49 + 7x) * (12 + -2x) (-49(12 + -2x) + 7x * (12 + -2x)) = 0 ((12 * -49 + -2x * -49) + 7x * (12 + -2x)) = 0 ((-588 + 98x) + 7x * (12 + -2x)) = 0 (-588 + 98x + (12 * 7x + -2x * 7x)) = 0 (-588 + 98x + (84x + -14x2)) = 0 Combine like terms: 98x + 84x = 182x (-588 + 182x + -14x2) = 0 Solving -588 + 182x + -14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '14'. 14(-42 + 13x + -1x2) = 0 Factor a trinomial. 14((-7 + x)(6 + -1x)) = 0 Ignore the factor 14.Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 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 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Simplifying x = 7Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {7, 6}
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