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Simplifying (8z + -3)(3z + 4) = (6z + -5)(4z + 9) Reorder the terms: (-3 + 8z)(3z + 4) = (6z + -5)(4z + 9) Reorder the terms: (-3 + 8z)(4 + 3z) = (6z + -5)(4z + 9) Multiply (-3 + 8z) * (4 + 3z) (-3(4 + 3z) + 8z * (4 + 3z)) = (6z + -5)(4z + 9) ((4 * -3 + 3z * -3) + 8z * (4 + 3z)) = (6z + -5)(4z + 9) ((-12 + -9z) + 8z * (4 + 3z)) = (6z + -5)(4z + 9) (-12 + -9z + (4 * 8z + 3z * 8z)) = (6z + -5)(4z + 9) (-12 + -9z + (32z + 24z2)) = (6z + -5)(4z + 9) Combine like terms: -9z + 32z = 23z (-12 + 23z + 24z2) = (6z + -5)(4z + 9) Reorder the terms: -12 + 23z + 24z2 = (-5 + 6z)(4z + 9) Reorder the terms: -12 + 23z + 24z2 = (-5 + 6z)(9 + 4z) Multiply (-5 + 6z) * (9 + 4z) -12 + 23z + 24z2 = (-5(9 + 4z) + 6z * (9 + 4z)) -12 + 23z + 24z2 = ((9 * -5 + 4z * -5) + 6z * (9 + 4z)) -12 + 23z + 24z2 = ((-45 + -20z) + 6z * (9 + 4z)) -12 + 23z + 24z2 = (-45 + -20z + (9 * 6z + 4z * 6z)) -12 + 23z + 24z2 = (-45 + -20z + (54z + 24z2)) Combine like terms: -20z + 54z = 34z -12 + 23z + 24z2 = (-45 + 34z + 24z2) Add '-24z2' to each side of the equation. -12 + 23z + 24z2 + -24z2 = -45 + 34z + 24z2 + -24z2 Combine like terms: 24z2 + -24z2 = 0 -12 + 23z + 0 = -45 + 34z + 24z2 + -24z2 -12 + 23z = -45 + 34z + 24z2 + -24z2 Combine like terms: 24z2 + -24z2 = 0 -12 + 23z = -45 + 34z + 0 -12 + 23z = -45 + 34z Solving -12 + 23z = -45 + 34z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-34z' to each side of the equation. -12 + 23z + -34z = -45 + 34z + -34z Combine like terms: 23z + -34z = -11z -12 + -11z = -45 + 34z + -34z Combine like terms: 34z + -34z = 0 -12 + -11z = -45 + 0 -12 + -11z = -45 Add '12' to each side of the equation. -12 + 12 + -11z = -45 + 12 Combine like terms: -12 + 12 = 0 0 + -11z = -45 + 12 -11z = -45 + 12 Combine like terms: -45 + 12 = -33 -11z = -33 Divide each side by '-11'. z = 3 Simplifying z = 3
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