x(4x-5)-(2x-7)(3x+2)=

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Solution for x(4x-5)-(2x-7)(3x+2)= equation:


Simplifying
x(4x + -5) + -1(2x + -7)(3x + 2) = 0

Reorder the terms:
x(-5 + 4x) + -1(2x + -7)(3x + 2) = 0
(-5 * x + 4x * x) + -1(2x + -7)(3x + 2) = 0
(-5x + 4x2) + -1(2x + -7)(3x + 2) = 0

Reorder the terms:
-5x + 4x2 + -1(-7 + 2x)(3x + 2) = 0

Reorder the terms:
-5x + 4x2 + -1(-7 + 2x)(2 + 3x) = 0

Multiply (-7 + 2x) * (2 + 3x)
-5x + 4x2 + -1(-7(2 + 3x) + 2x * (2 + 3x)) = 0
-5x + 4x2 + -1((2 * -7 + 3x * -7) + 2x * (2 + 3x)) = 0
-5x + 4x2 + -1((-14 + -21x) + 2x * (2 + 3x)) = 0
-5x + 4x2 + -1(-14 + -21x + (2 * 2x + 3x * 2x)) = 0
-5x + 4x2 + -1(-14 + -21x + (4x + 6x2)) = 0

Combine like terms: -21x + 4x = -17x
-5x + 4x2 + -1(-14 + -17x + 6x2) = 0
-5x + 4x2 + (-14 * -1 + -17x * -1 + 6x2 * -1) = 0
-5x + 4x2 + (14 + 17x + -6x2) = 0

Reorder the terms:
14 + -5x + 17x + 4x2 + -6x2 = 0

Combine like terms: -5x + 17x = 12x
14 + 12x + 4x2 + -6x2 = 0

Combine like terms: 4x2 + -6x2 = -2x2
14 + 12x + -2x2 = 0

Solving
14 + 12x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 6x + -1x2) = 0

Factor a trinomial.
2((7 + -1x)(1 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {7, -1}

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