0=7x^2-30x+27

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Solution for 0=7x^2-30x+27 equation:


Simplifying
0 = 7x2 + -30x + 27

Reorder the terms:
0 = 27 + -30x + 7x2

Solving
0 = 27 + -30x + 7x2

Solving for variable 'x'.

Combine like terms: 0 + -27 = -27
-27 + 30x + -7x2 = 27 + -30x + 7x2 + -27 + 30x + -7x2

Reorder the terms:
-27 + 30x + -7x2 = 27 + -27 + -30x + 30x + 7x2 + -7x2

Combine like terms: 27 + -27 = 0
-27 + 30x + -7x2 = 0 + -30x + 30x + 7x2 + -7x2
-27 + 30x + -7x2 = -30x + 30x + 7x2 + -7x2

Combine like terms: -30x + 30x = 0
-27 + 30x + -7x2 = 0 + 7x2 + -7x2
-27 + 30x + -7x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-27 + 30x + -7x2 = 0

Factor a trinomial.
(-3 + x)(9 + -7x) = 0

Subproblem 1

Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3

Subproblem 2

Set the factor '(9 + -7x)' equal to zero and attempt to solve: Simplifying 9 + -7x = 0 Solving 9 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -7x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -7x = 0 + -9 -7x = 0 + -9 Combine like terms: 0 + -9 = -9 -7x = -9 Divide each side by '-7'. x = 1.285714286 Simplifying x = 1.285714286

Solution

x = {3, 1.285714286}

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