(3x-4)(x+2)-7x+10=0

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Solution for (3x-4)(x+2)-7x+10=0 equation: 


Simplifying
(3x + -4)(x + 2) + -7x + 10 = 0

Reorder the terms:
(-4 + 3x)(x + 2) + -7x + 10 = 0

Reorder the terms:
(-4 + 3x)(2 + x) + -7x + 10 = 0

Multiply (-4 + 3x) * (2 + x)
(-4(2 + x) + 3x * (2 + x)) + -7x + 10 = 0
((2 * -4 + x * -4) + 3x * (2 + x)) + -7x + 10 = 0
((-8 + -4x) + 3x * (2 + x)) + -7x + 10 = 0
(-8 + -4x + (2 * 3x + x * 3x)) + -7x + 10 = 0
(-8 + -4x + (6x + 3x2)) + -7x + 10 = 0

Combine like terms: -4x + 6x = 2x
(-8 + 2x + 3x2) + -7x + 10 = 0

Reorder the terms:
-8 + 10 + 2x + -7x + 3x2 = 0

Combine like terms: -8 + 10 = 2
2 + 2x + -7x + 3x2 = 0

Combine like terms: 2x + -7x = -5x
2 + -5x + 3x2 = 0

Solving
2 + -5x + 3x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {0.6666666667, 1}

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