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Simplifying x(5x + -3) + x(4x + -2) = (9x + 5)(x + -1) Reorder the terms: x(-3 + 5x) + x(4x + -2) = (9x + 5)(x + -1) (-3 * x + 5x * x) + x(4x + -2) = (9x + 5)(x + -1) (-3x + 5x2) + x(4x + -2) = (9x + 5)(x + -1) Reorder the terms: -3x + 5x2 + x(-2 + 4x) = (9x + 5)(x + -1) -3x + 5x2 + (-2 * x + 4x * x) = (9x + 5)(x + -1) -3x + 5x2 + (-2x + 4x2) = (9x + 5)(x + -1) Reorder the terms: -3x + -2x + 5x2 + 4x2 = (9x + 5)(x + -1) Combine like terms: -3x + -2x = -5x -5x + 5x2 + 4x2 = (9x + 5)(x + -1) Combine like terms: 5x2 + 4x2 = 9x2 -5x + 9x2 = (9x + 5)(x + -1) Reorder the terms: -5x + 9x2 = (5 + 9x)(x + -1) Reorder the terms: -5x + 9x2 = (5 + 9x)(-1 + x) Multiply (5 + 9x) * (-1 + x) -5x + 9x2 = (5(-1 + x) + 9x * (-1 + x)) -5x + 9x2 = ((-1 * 5 + x * 5) + 9x * (-1 + x)) -5x + 9x2 = ((-5 + 5x) + 9x * (-1 + x)) -5x + 9x2 = (-5 + 5x + (-1 * 9x + x * 9x)) -5x + 9x2 = (-5 + 5x + (-9x + 9x2)) Combine like terms: 5x + -9x = -4x -5x + 9x2 = (-5 + -4x + 9x2) Add '-9x2' to each side of the equation. -5x + 9x2 + -9x2 = -5 + -4x + 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -5x + 0 = -5 + -4x + 9x2 + -9x2 -5x = -5 + -4x + 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -5x = -5 + -4x + 0 -5x = -5 + -4x Solving -5x = -5 + -4x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4x' to each side of the equation. -5x + 4x = -5 + -4x + 4x Combine like terms: -5x + 4x = -1x -1x = -5 + -4x + 4x Combine like terms: -4x + 4x = 0 -1x = -5 + 0 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5
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