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Simplifying (-7x + 7)(-4x + -6) = -7x + 7 Reorder the terms: (7 + -7x)(-4x + -6) = -7x + 7 Reorder the terms: (7 + -7x)(-6 + -4x) = -7x + 7 Multiply (7 + -7x) * (-6 + -4x) (7(-6 + -4x) + -7x * (-6 + -4x)) = -7x + 7 ((-6 * 7 + -4x * 7) + -7x * (-6 + -4x)) = -7x + 7 ((-42 + -28x) + -7x * (-6 + -4x)) = -7x + 7 (-42 + -28x + (-6 * -7x + -4x * -7x)) = -7x + 7 (-42 + -28x + (42x + 28x2)) = -7x + 7 Combine like terms: -28x + 42x = 14x (-42 + 14x + 28x2) = -7x + 7 Reorder the terms: -42 + 14x + 28x2 = 7 + -7x Solving -42 + 14x + 28x2 = 7 + -7x Solving for variable 'x'. Reorder the terms: -42 + -7 + 14x + 7x + 28x2 = 7 + -7x + -7 + 7x Combine like terms: -42 + -7 = -49 -49 + 14x + 7x + 28x2 = 7 + -7x + -7 + 7x Combine like terms: 14x + 7x = 21x -49 + 21x + 28x2 = 7 + -7x + -7 + 7x Reorder the terms: -49 + 21x + 28x2 = 7 + -7 + -7x + 7x Combine like terms: 7 + -7 = 0 -49 + 21x + 28x2 = 0 + -7x + 7x -49 + 21x + 28x2 = -7x + 7x Combine like terms: -7x + 7x = 0 -49 + 21x + 28x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-7 + 3x + 4x2) = 0 Factor a trinomial. 7((-7 + -4x)(1 + -1x)) = 0 Ignore the factor 7.Subproblem 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 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-1.75, 1}
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