10=4x^2-7x+8

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Solution for 10=4x^2-7x+8 equation: 


Simplifying
10 = 4x2 + -7x + 8

Reorder the terms:
10 = 8 + -7x + 4x2

Solving
10 = 8 + -7x + 4x2

Solving for variable 'x'.

Combine like terms: 10 + -8 = 2
2 + 7x + -4x2 = 8 + -7x + 4x2 + -8 + 7x + -4x2

Reorder the terms:
2 + 7x + -4x2 = 8 + -8 + -7x + 7x + 4x2 + -4x2

Combine like terms: 8 + -8 = 0
2 + 7x + -4x2 = 0 + -7x + 7x + 4x2 + -4x2
2 + 7x + -4x2 = -7x + 7x + 4x2 + -4x2

Combine like terms: -7x + 7x = 0
2 + 7x + -4x2 = 0 + 4x2 + -4x2
2 + 7x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
2 + 7x + -4x2 = 0

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


Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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 = {2, -0.25}

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