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Simplifying (x + 7)(4x + -3) = (2x + 5)(2x + 3) Reorder the terms: (7 + x)(4x + -3) = (2x + 5)(2x + 3) Reorder the terms: (7 + x)(-3 + 4x) = (2x + 5)(2x + 3) Multiply (7 + x) * (-3 + 4x) (7(-3 + 4x) + x(-3 + 4x)) = (2x + 5)(2x + 3) ((-3 * 7 + 4x * 7) + x(-3 + 4x)) = (2x + 5)(2x + 3) ((-21 + 28x) + x(-3 + 4x)) = (2x + 5)(2x + 3) (-21 + 28x + (-3 * x + 4x * x)) = (2x + 5)(2x + 3) (-21 + 28x + (-3x + 4x2)) = (2x + 5)(2x + 3) Combine like terms: 28x + -3x = 25x (-21 + 25x + 4x2) = (2x + 5)(2x + 3) Reorder the terms: -21 + 25x + 4x2 = (5 + 2x)(2x + 3) Reorder the terms: -21 + 25x + 4x2 = (5 + 2x)(3 + 2x) Multiply (5 + 2x) * (3 + 2x) -21 + 25x + 4x2 = (5(3 + 2x) + 2x * (3 + 2x)) -21 + 25x + 4x2 = ((3 * 5 + 2x * 5) + 2x * (3 + 2x)) -21 + 25x + 4x2 = ((15 + 10x) + 2x * (3 + 2x)) -21 + 25x + 4x2 = (15 + 10x + (3 * 2x + 2x * 2x)) -21 + 25x + 4x2 = (15 + 10x + (6x + 4x2)) Combine like terms: 10x + 6x = 16x -21 + 25x + 4x2 = (15 + 16x + 4x2) Add '-4x2' to each side of the equation. -21 + 25x + 4x2 + -4x2 = 15 + 16x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -21 + 25x + 0 = 15 + 16x + 4x2 + -4x2 -21 + 25x = 15 + 16x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -21 + 25x = 15 + 16x + 0 -21 + 25x = 15 + 16x Solving -21 + 25x = 15 + 16x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16x' to each side of the equation. -21 + 25x + -16x = 15 + 16x + -16x Combine like terms: 25x + -16x = 9x -21 + 9x = 15 + 16x + -16x Combine like terms: 16x + -16x = 0 -21 + 9x = 15 + 0 -21 + 9x = 15 Add '21' to each side of the equation. -21 + 21 + 9x = 15 + 21 Combine like terms: -21 + 21 = 0 0 + 9x = 15 + 21 9x = 15 + 21 Combine like terms: 15 + 21 = 36 9x = 36 Divide each side by '9'. x = 4 Simplifying x = 4
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