6x^2+62x+20=14x^2+24x+10

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Solution for 6x^2+62x+20=14x^2+24x+10 equation:


Simplifying
6x2 + 62x + 20 = 14x2 + 24x + 10

Reorder the terms:
20 + 62x + 6x2 = 14x2 + 24x + 10

Reorder the terms:
20 + 62x + 6x2 = 10 + 24x + 14x2

Solving
20 + 62x + 6x2 = 10 + 24x + 14x2

Solving for variable 'x'.

Reorder the terms:
20 + -10 + 62x + -24x + 6x2 + -14x2 = 10 + 24x + 14x2 + -10 + -24x + -14x2

Combine like terms: 20 + -10 = 10
10 + 62x + -24x + 6x2 + -14x2 = 10 + 24x + 14x2 + -10 + -24x + -14x2

Combine like terms: 62x + -24x = 38x
10 + 38x + 6x2 + -14x2 = 10 + 24x + 14x2 + -10 + -24x + -14x2

Combine like terms: 6x2 + -14x2 = -8x2
10 + 38x + -8x2 = 10 + 24x + 14x2 + -10 + -24x + -14x2

Reorder the terms:
10 + 38x + -8x2 = 10 + -10 + 24x + -24x + 14x2 + -14x2

Combine like terms: 10 + -10 = 0
10 + 38x + -8x2 = 0 + 24x + -24x + 14x2 + -14x2
10 + 38x + -8x2 = 24x + -24x + 14x2 + -14x2

Combine like terms: 24x + -24x = 0
10 + 38x + -8x2 = 0 + 14x2 + -14x2
10 + 38x + -8x2 = 14x2 + -14x2

Combine like terms: 14x2 + -14x2 = 0
10 + 38x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 19x + -4x2) = 0

Factor a trinomial.
2((5 + -1x)(1 + 4x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Subproblem 2

Set the factor '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 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 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25

Solution

x = {5, -0.25}

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