51-z(3z+4)=2(17-2z)-58

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Solution for 51-z(3z+4)=2(17-2z)-58 equation:


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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