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Simplifying 51 + -1z(3z + 4) = 2(17 + -2z) + -58 Reorder the terms: 51 + -1z(4 + 3z) = 2(17 + -2z) + -58 51 + (4 * -1z + 3z * -1z) = 2(17 + -2z) + -58 51 + (-4z + -3z2) = 2(17 + -2z) + -58 51 + -4z + -3z2 = (17 * 2 + -2z * 2) + -58 51 + -4z + -3z2 = (34 + -4z) + -58 Reorder the terms: 51 + -4z + -3z2 = 34 + -58 + -4z Combine like terms: 34 + -58 = -24 51 + -4z + -3z2 = -24 + -4z Add '4z' to each side of the equation. 51 + -4z + 4z + -3z2 = -24 + -4z + 4z Combine like terms: -4z + 4z = 0 51 + 0 + -3z2 = -24 + -4z + 4z 51 + -3z2 = -24 + -4z + 4z Combine like terms: -4z + 4z = 0 51 + -3z2 = -24 + 0 51 + -3z2 = -24 Solving 51 + -3z2 = -24 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-51' to each side of the equation. 51 + -51 + -3z2 = -24 + -51 Combine like terms: 51 + -51 = 0 0 + -3z2 = -24 + -51 -3z2 = -24 + -51 Combine like terms: -24 + -51 = -75 -3z2 = -75 Divide each side by '-3'. z2 = 25 Simplifying z2 = 25 Take the square root of each side: z = {-5, 5}
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