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Simplifying (2e + -3)(7 + 5e) = (10e + -4)(e + -3) Reorder the terms: (-3 + 2e)(7 + 5e) = (10e + -4)(e + -3) Multiply (-3 + 2e) * (7 + 5e) (-3(7 + 5e) + 2e * (7 + 5e)) = (10e + -4)(e + -3) ((7 * -3 + 5e * -3) + 2e * (7 + 5e)) = (10e + -4)(e + -3) ((-21 + -15e) + 2e * (7 + 5e)) = (10e + -4)(e + -3) (-21 + -15e + (7 * 2e + 5e * 2e)) = (10e + -4)(e + -3) (-21 + -15e + (14e + 10e2)) = (10e + -4)(e + -3) Combine like terms: -15e + 14e = -1e (-21 + -1e + 10e2) = (10e + -4)(e + -3) Reorder the terms: -21 + -1e + 10e2 = (-4 + 10e)(e + -3) Reorder the terms: -21 + -1e + 10e2 = (-4 + 10e)(-3 + e) Multiply (-4 + 10e) * (-3 + e) -21 + -1e + 10e2 = (-4(-3 + e) + 10e * (-3 + e)) -21 + -1e + 10e2 = ((-3 * -4 + e * -4) + 10e * (-3 + e)) -21 + -1e + 10e2 = ((12 + -4e) + 10e * (-3 + e)) -21 + -1e + 10e2 = (12 + -4e + (-3 * 10e + e * 10e)) -21 + -1e + 10e2 = (12 + -4e + (-30e + 10e2)) Combine like terms: -4e + -30e = -34e -21 + -1e + 10e2 = (12 + -34e + 10e2) Add '-10e2' to each side of the equation. -21 + -1e + 10e2 + -10e2 = 12 + -34e + 10e2 + -10e2 Combine like terms: 10e2 + -10e2 = 0 -21 + -1e + 0 = 12 + -34e + 10e2 + -10e2 -21 + -1e = 12 + -34e + 10e2 + -10e2 Combine like terms: 10e2 + -10e2 = 0 -21 + -1e = 12 + -34e + 0 -21 + -1e = 12 + -34e Solving -21 + -1e = 12 + -34e Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '34e' to each side of the equation. -21 + -1e + 34e = 12 + -34e + 34e Combine like terms: -1e + 34e = 33e -21 + 33e = 12 + -34e + 34e Combine like terms: -34e + 34e = 0 -21 + 33e = 12 + 0 -21 + 33e = 12 Add '21' to each side of the equation. -21 + 21 + 33e = 12 + 21 Combine like terms: -21 + 21 = 0 0 + 33e = 12 + 21 33e = 12 + 21 Combine like terms: 12 + 21 = 33 33e = 33 Divide each side by '33'. e = 1 Simplifying e = 1
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