10x^2+5-x-7=4x^2

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Solution for 10x^2+5-x-7=4x^2 equation:


Simplifying
10x2 + 5 + -1x + -7 = 4x2

Reorder the terms:
5 + -7 + -1x + 10x2 = 4x2

Combine like terms: 5 + -7 = -2
-2 + -1x + 10x2 = 4x2

Solving
-2 + -1x + 10x2 = 4x2

Solving for variable 'x'.

Combine like terms: 10x2 + -4x2 = 6x2
-2 + -1x + 6x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-2 + -1x + 6x2 = 0

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

Subproblem 1

Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5

Subproblem 2

Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667

Solution

x = {-0.5, 0.6666666667}

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