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Simplifying (4x + 5)(5x + -4) = x + 13 Reorder the terms: (5 + 4x)(5x + -4) = x + 13 Reorder the terms: (5 + 4x)(-4 + 5x) = x + 13 Multiply (5 + 4x) * (-4 + 5x) (5(-4 + 5x) + 4x * (-4 + 5x)) = x + 13 ((-4 * 5 + 5x * 5) + 4x * (-4 + 5x)) = x + 13 ((-20 + 25x) + 4x * (-4 + 5x)) = x + 13 (-20 + 25x + (-4 * 4x + 5x * 4x)) = x + 13 (-20 + 25x + (-16x + 20x2)) = x + 13 Combine like terms: 25x + -16x = 9x (-20 + 9x + 20x2) = x + 13 Reorder the terms: -20 + 9x + 20x2 = 13 + x Solving -20 + 9x + 20x2 = 13 + x Solving for variable 'x'. Reorder the terms: -20 + -13 + 9x + -1x + 20x2 = 13 + x + -13 + -1x Combine like terms: -20 + -13 = -33 -33 + 9x + -1x + 20x2 = 13 + x + -13 + -1x Combine like terms: 9x + -1x = 8x -33 + 8x + 20x2 = 13 + x + -13 + -1x Reorder the terms: -33 + 8x + 20x2 = 13 + -13 + x + -1x Combine like terms: 13 + -13 = 0 -33 + 8x + 20x2 = 0 + x + -1x -33 + 8x + 20x2 = x + -1x Combine like terms: x + -1x = 0 -33 + 8x + 20x2 = 0 Factor a trinomial. (-3 + -2x)(11 + -10x) = 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 '(11 + -10x)' equal to zero and attempt to solve: Simplifying 11 + -10x = 0 Solving 11 + -10x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -10x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -10x = 0 + -11 -10x = 0 + -11 Combine like terms: 0 + -11 = -11 -10x = -11 Divide each side by '-10'. x = 1.1 Simplifying x = 1.1Solution
x = {-1.5, 1.1}
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