-14x^2+98x=10x^2+88

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Solution for -14x^2+98x=10x^2+88 equation: 


Simplifying
-14x2 + 98x = 10x2 + 88

Reorder the terms:
98x + -14x2 = 10x2 + 88

Reorder the terms:
98x + -14x2 = 88 + 10x2

Solving
98x + -14x2 = 88 + 10x2

Solving for variable 'x'.

Reorder the terms:
-88 + 98x + -14x2 + -10x2 = 88 + 10x2 + -88 + -10x2

Combine like terms: -14x2 + -10x2 = -24x2
-88 + 98x + -24x2 = 88 + 10x2 + -88 + -10x2

Reorder the terms:
-88 + 98x + -24x2 = 88 + -88 + 10x2 + -10x2

Combine like terms: 88 + -88 = 0
-88 + 98x + -24x2 = 0 + 10x2 + -10x2
-88 + 98x + -24x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-88 + 98x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-44 + 49x + -12x2) = 0

Factor a trinomial.
2((-11 + 4x)(4 + -3x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-11 + 4x)' equal to zero and attempt to solve:

Simplifying
-11 + 4x = 0

Solving
-11 + 4x = 0

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

Add '11' to each side of the equation.
-11 + 11 + 4x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 4x = 0 + 11
4x = 0 + 11

Combine like terms: 0 + 11 = 11
4x = 11

Divide each side by '4'.
x = 2.75

Simplifying
x = 2.75

Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {2.75, 1.333333333}

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