14x^2=46x-12

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Solution for 14x^2=46x-12 equation:


Simplifying
14x2 = 46x + -12

Reorder the terms:
14x2 = -12 + 46x

Solving
14x2 = -12 + 46x

Solving for variable 'x'.

Reorder the terms:
12 + -46x + 14x2 = -12 + 46x + 12 + -46x

Reorder the terms:
12 + -46x + 14x2 = -12 + 12 + 46x + -46x

Combine like terms: -12 + 12 = 0
12 + -46x + 14x2 = 0 + 46x + -46x
12 + -46x + 14x2 = 46x + -46x

Combine like terms: 46x + -46x = 0
12 + -46x + 14x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -23x + 7x2) = 0

Factor a trinomial.
2((2 + -7x)(3 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(2 + -7x)' equal to zero and attempt to solve: Simplifying 2 + -7x = 0 Solving 2 + -7x = 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 + -7x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7x = 0 + -2 -7x = 0 + -2 Combine like terms: 0 + -2 = -2 -7x = -2 Divide each side by '-7'. x = 0.2857142857 Simplifying x = 0.2857142857

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {0.2857142857, 3}

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