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Simplifying (4x + -4)(2x + 7) = 0 Reorder the terms: (-4 + 4x)(2x + 7) = 0 Reorder the terms: (-4 + 4x)(7 + 2x) = 0 Multiply (-4 + 4x) * (7 + 2x) (-4(7 + 2x) + 4x * (7 + 2x)) = 0 ((7 * -4 + 2x * -4) + 4x * (7 + 2x)) = 0 ((-28 + -8x) + 4x * (7 + 2x)) = 0 (-28 + -8x + (7 * 4x + 2x * 4x)) = 0 (-28 + -8x + (28x + 8x2)) = 0 Combine like terms: -8x + 28x = 20x (-28 + 20x + 8x2) = 0 Solving -28 + 20x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-7 + 5x + 2x2) = 0 Factor a trinomial. 4((-7 + -2x)(1 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve: Simplifying -7 + -2x = 0 Solving -7 + -2x = 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 + -2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2x = 0 + 7 -2x = 0 + 7 Combine like terms: 0 + 7 = 7 -2x = 7 Divide each side by '-2'. x = -3.5 Simplifying x = -3.5Subproblem 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 = {-3.5, 1}
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