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Simplifying (4x + 3)(x + -5) = 8x + 6 Reorder the terms: (3 + 4x)(x + -5) = 8x + 6 Reorder the terms: (3 + 4x)(-5 + x) = 8x + 6 Multiply (3 + 4x) * (-5 + x) (3(-5 + x) + 4x * (-5 + x)) = 8x + 6 ((-5 * 3 + x * 3) + 4x * (-5 + x)) = 8x + 6 ((-15 + 3x) + 4x * (-5 + x)) = 8x + 6 (-15 + 3x + (-5 * 4x + x * 4x)) = 8x + 6 (-15 + 3x + (-20x + 4x2)) = 8x + 6 Combine like terms: 3x + -20x = -17x (-15 + -17x + 4x2) = 8x + 6 Reorder the terms: -15 + -17x + 4x2 = 6 + 8x Solving -15 + -17x + 4x2 = 6 + 8x Solving for variable 'x'. Reorder the terms: -15 + -6 + -17x + -8x + 4x2 = 6 + 8x + -6 + -8x Combine like terms: -15 + -6 = -21 -21 + -17x + -8x + 4x2 = 6 + 8x + -6 + -8x Combine like terms: -17x + -8x = -25x -21 + -25x + 4x2 = 6 + 8x + -6 + -8x Reorder the terms: -21 + -25x + 4x2 = 6 + -6 + 8x + -8x Combine like terms: 6 + -6 = 0 -21 + -25x + 4x2 = 0 + 8x + -8x -21 + -25x + 4x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -21 + -25x + 4x2 = 0 Factor a trinomial. (-3 + -4x)(7 + -1x) = 0Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve: Simplifying -3 + -4x = 0 Solving -3 + -4x = 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 + -4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4x = 0 + 3 -4x = 0 + 3 Combine like terms: 0 + 3 = 3 -4x = 3 Divide each side by '-4'. x = -0.75 Simplifying x = -0.75Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {-0.75, 7}
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