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Simplifying (5z + -7)(4z + 5) = 10z(2z + -1) Reorder the terms: (-7 + 5z)(4z + 5) = 10z(2z + -1) Reorder the terms: (-7 + 5z)(5 + 4z) = 10z(2z + -1) Multiply (-7 + 5z) * (5 + 4z) (-7(5 + 4z) + 5z * (5 + 4z)) = 10z(2z + -1) ((5 * -7 + 4z * -7) + 5z * (5 + 4z)) = 10z(2z + -1) ((-35 + -28z) + 5z * (5 + 4z)) = 10z(2z + -1) (-35 + -28z + (5 * 5z + 4z * 5z)) = 10z(2z + -1) (-35 + -28z + (25z + 20z2)) = 10z(2z + -1) Combine like terms: -28z + 25z = -3z (-35 + -3z + 20z2) = 10z(2z + -1) Reorder the terms: -35 + -3z + 20z2 = 10z(-1 + 2z) -35 + -3z + 20z2 = (-1 * 10z + 2z * 10z) -35 + -3z + 20z2 = (-10z + 20z2) Add '-20z2' to each side of the equation. -35 + -3z + 20z2 + -20z2 = -10z + 20z2 + -20z2 Combine like terms: 20z2 + -20z2 = 0 -35 + -3z + 0 = -10z + 20z2 + -20z2 -35 + -3z = -10z + 20z2 + -20z2 Combine like terms: 20z2 + -20z2 = 0 -35 + -3z = -10z + 0 -35 + -3z = -10z Solving -35 + -3z = -10z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '10z' to each side of the equation. -35 + -3z + 10z = -10z + 10z Combine like terms: -3z + 10z = 7z -35 + 7z = -10z + 10z Combine like terms: -10z + 10z = 0 -35 + 7z = 0 Add '35' to each side of the equation. -35 + 35 + 7z = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 7z = 0 + 35 7z = 0 + 35 Combine like terms: 0 + 35 = 35 7z = 35 Divide each side by '7'. z = 5 Simplifying z = 5
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