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Simplifying 10(5z + -4) + 15(2 + -6z) = 6(1 + -4z) Reorder the terms: 10(-4 + 5z) + 15(2 + -6z) = 6(1 + -4z) (-4 * 10 + 5z * 10) + 15(2 + -6z) = 6(1 + -4z) (-40 + 50z) + 15(2 + -6z) = 6(1 + -4z) -40 + 50z + (2 * 15 + -6z * 15) = 6(1 + -4z) -40 + 50z + (30 + -90z) = 6(1 + -4z) Reorder the terms: -40 + 30 + 50z + -90z = 6(1 + -4z) Combine like terms: -40 + 30 = -10 -10 + 50z + -90z = 6(1 + -4z) Combine like terms: 50z + -90z = -40z -10 + -40z = 6(1 + -4z) -10 + -40z = (1 * 6 + -4z * 6) -10 + -40z = (6 + -24z) Solving -10 + -40z = 6 + -24z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '24z' to each side of the equation. -10 + -40z + 24z = 6 + -24z + 24z Combine like terms: -40z + 24z = -16z -10 + -16z = 6 + -24z + 24z Combine like terms: -24z + 24z = 0 -10 + -16z = 6 + 0 -10 + -16z = 6 Add '10' to each side of the equation. -10 + 10 + -16z = 6 + 10 Combine like terms: -10 + 10 = 0 0 + -16z = 6 + 10 -16z = 6 + 10 Combine like terms: 6 + 10 = 16 -16z = 16 Divide each side by '-16'. z = -1 Simplifying z = -1
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