6x(x-5)+14=2(x-6)

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Solution for 6x(x-5)+14=2(x-6) equation: 


Simplifying
6x(x + -5) + 14 = 2(x + -6)

Reorder the terms:
6x(-5 + x) + 14 = 2(x + -6)
(-5 * 6x + x * 6x) + 14 = 2(x + -6)
(-30x + 6x2) + 14 = 2(x + -6)

Reorder the terms:
14 + -30x + 6x2 = 2(x + -6)

Reorder the terms:
14 + -30x + 6x2 = 2(-6 + x)
14 + -30x + 6x2 = (-6 * 2 + x * 2)
14 + -30x + 6x2 = (-12 + 2x)

Solving
14 + -30x + 6x2 = -12 + 2x

Solving for variable 'x'.

Reorder the terms:
14 + 12 + -30x + -2x + 6x2 = -12 + 2x + 12 + -2x

Combine like terms: 14 + 12 = 26
26 + -30x + -2x + 6x2 = -12 + 2x + 12 + -2x

Combine like terms: -30x + -2x = -32x
26 + -32x + 6x2 = -12 + 2x + 12 + -2x

Reorder the terms:
26 + -32x + 6x2 = -12 + 12 + 2x + -2x

Combine like terms: -12 + 12 = 0
26 + -32x + 6x2 = 0 + 2x + -2x
26 + -32x + 6x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
26 + -32x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(13 + -16x + 3x2) = 0

Factor a trinomial.
2((1 + -1x)(13 + -3x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1

Subproblem 2
Set the factor '(13 + -3x)' equal to zero and attempt to solve:

Simplifying
13 + -3x = 0

Solving
13 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-13' to each side of the equation.
13 + -13 + -3x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -3x = 0 + -13
-3x = 0 + -13

Combine like terms: 0 + -13 = -13
-3x = -13

Divide each side by '-3'.
x = 4.333333333

Simplifying
x = 4.333333333
Solution
x = {1, 4.333333333}

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