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Simplifying (2x + -7)(x + -3) = 6 Reorder the terms: (-7 + 2x)(x + -3) = 6 Reorder the terms: (-7 + 2x)(-3 + x) = 6 Multiply (-7 + 2x) * (-3 + x) (-7(-3 + x) + 2x * (-3 + x)) = 6 ((-3 * -7 + x * -7) + 2x * (-3 + x)) = 6 ((21 + -7x) + 2x * (-3 + x)) = 6 (21 + -7x + (-3 * 2x + x * 2x)) = 6 (21 + -7x + (-6x + 2x2)) = 6 Combine like terms: -7x + -6x = -13x (21 + -13x + 2x2) = 6 Solving 21 + -13x + 2x2 = 6 Solving for variable 'x'. Reorder the terms: 21 + -6 + -13x + 2x2 = 6 + -6 Combine like terms: 21 + -6 = 15 15 + -13x + 2x2 = 6 + -6 Combine like terms: 6 + -6 = 0 15 + -13x + 2x2 = 0 Factor a trinomial. (3 + -2x)(5 + -1x) = 0Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {1.5, 5}
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