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Simplifying (5z + 2a)(3z + 4b) = 8ab Reorder the terms: (2a + 5z)(3z + 4b) = 8ab Reorder the terms: (2a + 5z)(4b + 3z) = 8ab Multiply (2a + 5z) * (4b + 3z) (2a * (4b + 3z) + 5z * (4b + 3z)) = 8ab ((4b * 2a + 3z * 2a) + 5z * (4b + 3z)) = 8ab ((8ab + 6az) + 5z * (4b + 3z)) = 8ab (8ab + 6az + (4b * 5z + 3z * 5z)) = 8ab (8ab + 6az + (20bz + 15z2)) = 8ab (8ab + 6az + 20bz + 15z2) = 8ab Add '-8ab' to each side of the equation. 8ab + 6az + 20bz + -8ab + 15z2 = 8ab + -8ab Reorder the terms: 8ab + -8ab + 6az + 20bz + 15z2 = 8ab + -8ab Combine like terms: 8ab + -8ab = 0 0 + 6az + 20bz + 15z2 = 8ab + -8ab 6az + 20bz + 15z2 = 8ab + -8ab Combine like terms: 8ab + -8ab = 0 6az + 20bz + 15z2 = 0 Solving 6az + 20bz + 15z2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-20bz' to each side of the equation. 6az + 20bz + -20bz + 15z2 = 0 + -20bz Combine like terms: 20bz + -20bz = 0 6az + 0 + 15z2 = 0 + -20bz 6az + 15z2 = 0 + -20bz Remove the zero: 6az + 15z2 = -20bz Add '-15z2' to each side of the equation. 6az + 15z2 + -15z2 = -20bz + -15z2 Combine like terms: 15z2 + -15z2 = 0 6az + 0 = -20bz + -15z2 6az = -20bz + -15z2 Divide each side by '6z'. a = -3.333333333b + -2.5z Simplifying a = -3.333333333b + -2.5z
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