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Simplifying (7 + -1x)(-4 + -1x) = 2 + -4x Multiply (7 + -1x) * (-4 + -1x) (7(-4 + -1x) + -1x * (-4 + -1x)) = 2 + -4x ((-4 * 7 + -1x * 7) + -1x * (-4 + -1x)) = 2 + -4x ((-28 + -7x) + -1x * (-4 + -1x)) = 2 + -4x (-28 + -7x + (-4 * -1x + -1x * -1x)) = 2 + -4x (-28 + -7x + (4x + 1x2)) = 2 + -4x Combine like terms: -7x + 4x = -3x (-28 + -3x + 1x2) = 2 + -4x Solving -28 + -3x + 1x2 = 2 + -4x Solving for variable 'x'. Reorder the terms: -28 + -2 + -3x + 4x + 1x2 = 2 + -4x + -2 + 4x Combine like terms: -28 + -2 = -30 -30 + -3x + 4x + 1x2 = 2 + -4x + -2 + 4x Combine like terms: -3x + 4x = 1x -30 + 1x + 1x2 = 2 + -4x + -2 + 4x Reorder the terms: -30 + 1x + 1x2 = 2 + -2 + -4x + 4x Combine like terms: 2 + -2 = 0 -30 + 1x + 1x2 = 0 + -4x + 4x -30 + 1x + 1x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -30 + 1x + 1x2 = 0 Factor a trinomial. (-6 + -1x)(5 + -1x) = 0Subproblem 1
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 = -6Subproblem 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 = {-6, 5}
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