6x^2-28x=-32

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Solution for 6x^2-28x=-32 equation:


Simplifying
6x2 + -28x = -32

Reorder the terms:
-28x + 6x2 = -32

Solving
-28x + 6x2 = -32

Solving for variable 'x'.

Reorder the terms:
32 + -28x + 6x2 = -32 + 32

Combine like terms: -32 + 32 = 0
32 + -28x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -14x + 3x2) = 0

Factor a trinomial.
2((2 + -1x)(8 + -3x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Subproblem 2

Set the factor '(8 + -3x)' equal to zero and attempt to solve: Simplifying 8 + -3x = 0 Solving 8 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3x = 0 + -8 -3x = 0 + -8 Combine like terms: 0 + -8 = -8 -3x = -8 Divide each side by '-3'. x = 2.666666667 Simplifying x = 2.666666667

Solution

x = {2, 2.666666667}

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