4x^2-2=10x-8

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Solution for 4x^2-2=10x-8 equation:


Simplifying
4x2 + -2 = 10x + -8

Reorder the terms:
-2 + 4x2 = 10x + -8

Reorder the terms:
-2 + 4x2 = -8 + 10x

Solving
-2 + 4x2 = -8 + 10x

Solving for variable 'x'.

Reorder the terms:
-2 + 8 + -10x + 4x2 = -8 + 10x + 8 + -10x

Combine like terms: -2 + 8 = 6
6 + -10x + 4x2 = -8 + 10x + 8 + -10x

Reorder the terms:
6 + -10x + 4x2 = -8 + 8 + 10x + -10x

Combine like terms: -8 + 8 = 0
6 + -10x + 4x2 = 0 + 10x + -10x
6 + -10x + 4x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
6 + -10x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -5x + 2x2) = 0

Factor a trinomial.
2((1 + -1x)(3 + -2x)) = 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 '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5

Solution

x = {1, 1.5}

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